The fundamental meaning of "discursive violence" is, as you might expect, simply "violence that occurs in written or spoken discourse rather than being acted out physically in the real world." The first instance that a Google Books search of the term bears out this primitive notion. From Oliver Elton, "Views and Reviews: Essays in Appreciation, By W.E. Henley," reviewed in The Academy, volume 38 (October 11, 1890):
The worst complaint that can be made against Mr. Henley is a certain violence of prejudice. The conduct of a partisan newspaper is the worst training in the world for a literary critic. A good critic like Mr. Henley is far too good for such a work, which he has lately undertaken ; and it is only surprising that he has suffered so little. But why should noisy prejudice be brought at all into the calm and grave senate-house of literature? The great writers who sit above are only grieved and surprised as they look down and behold these strange heats, this discursive violence. Why, for instance, should we be told about Benjamin Disraeli that he was "the antithesis of Grocerdom, the Satan of that revolt against the yielding habit of Jehova-Bottles, the spirit whereof is fast coming to be our one defence against socialism and the dominion of the Common Fool"? When a writer gives way in this fashion, style and matter deteriorate together.
The next result (chronologically) that Google Books offers comes 79 years later. It's a snippet from Marcel Brion, The Medici: A Great Florentine Family (1969), which again uses "discursive" in opposition to "actual":
The mass may be persuaded to give support to active violence (as it did to Michele di Lando during the Ciompi uprising), or to discursive violence (as it did later to Savonarola's fiery sermons), but prestige won by such precarious, accidental
At some point in the next decade or so, however, academics commandeered the phrase "discursive violence" and put it to labor for their own semiotic and gender-and-race-studies purposes. It has been theirs ever since. From Frank Burton, "Questions of Violence in Party Political Criminology," in Radical Issues in Criminology (1980):
These are the dominant paradigms in a text [by Georges Sorel, it seems] that is also a remarkable monument to ill-tempered political chatter and ad hominem attacks on parliamentary opponents managed through a syntax of discursive violence. Excesses, absurdities and incoherences aside, the signifiers of catharsis, bonding and transcendence have cut out a space for themselves in the languages of violence.
Wladimir Krysinski, "Manifestos, Avant-gardes, and Transgressive Modernity," in Aims and Prospects in Semiotics: Essays in Honor of Algirdas Julien Greimas (1985):
If such is one of the paradoxes of avant-garde dialectics, we have no alternative but to recognize that the new is closely linked to the symbolic violation using codes accomplished discursively by the manifestos. These codes, obviously, are in statu nascendi, but the manifestos have this in particular that they produce both recurrent semic categories and rules for the functioning of future artistic messages. Thus, when reduced to their dominating function in the social sphere where horizons of expectation and the forces determining the admissibility of ideological as well as aesthetic messages overlap, exclude and confront each other, the manifestos become semiotic laboratories. They manufacture a kind of "ready-made" codes by means of discursive violence so as to ensure the mutation and the admissibility of the values they advocate using the discursive procedures whose polyvalence we have analysed. Although the avant-garde codes may appear to be ephemeral, comprising a sizable polemical, meta-textual component, one can see how they are strengthened and become stable the moment avant-garde achievements are converted into acknowledged value.
David Garland, Punishment and Welfare: A History of Penal Strategies (1987) [snippet]:
Thus we find the frequent deployment of a kind of discursive violence [italics in original] whenever harsh measures need to be powerfully justified. And of course these emotive and alarmist descriptions of criminality go a long way toward explaining the deep sense of social threat and danger evoked by the imaginary figure of the criminal — both then and now. The following are only the most striking instances of violence that is pervasive in this discourse.
From Semiotics 1988 (September 1988) [snippet]:
Milton is imposing a private doctrinal emphasis on the mythic model of "War in Heaven," communicating the empowering unity of heaven's forces as signified through the dismemberment of the (literally) divided and self-interested rebels. John M. Steadman has observed a regular tendency among certain Renaissance writers towards discursive violence, ordinarily characterized by disruptive substitutions, as "for harmony, deliberate dismemberment, a kind of syntactic sparagmos" (1984 25).
(By the way, Steadman doesn't appear to use the term himself in the vicinity of the quoted passage, as who would who already had syntactic sparagmos on his plate?)
From Iris, issues 8–9 (1988) [snippet]:
The montage sequence compresses into a flurry of images the terms for a scene in which Helen can take her symbolically legitimate place. The difference of the montage sequence from the narrative context is the mark of the discursive violence required to set those terms. Violence, because Helen's return to the place of the image means returning to a place that is dominated by forces beyond her control. Violence, because Blonde Venus is itself the product of the dominated apparatus of fantasy that is Hollywood, and is the site of contention between broad social vision and a narrow ability to utter it.
From Studies in Twentieth Century Literature, volume 13, issue 2 (1989) [snippet]:
I would add that what is subverted must also include ideological constructions of gender. Yet the real—the legacy of familial discourse—however distanced and subverted it may be in modernist prose, can return in the very act that seemingly destabilizes it. Whence the ambiguity of this type of discursive violence. As I stated above, modernist textual fragmentation remains very much indebted to traditional familial figuration that restores a discursive continuity at another level.
So what precisely do these massed academics think "discursive violence" means? Perhaps it is best to let them speak for themselves (especially since, that way, we can also learn what they think "discursivity" means). From John Paul Jones, Heidi J. Nast, and Susan M. Roberts, contribution to Thresholds in Feminist Geography: Difference, Methodology, Representation (1997):
We define discursivity as those processes and practices through which statements are made, recorded, and legitimated through linguistic and other means of circulation. Discursive violence, then, involves using these processes and practices to script groups or persons in places, and in ways that counter how they would define themselves. In the process, discursive violence obscures the socio-spatial relations through which a group is subordinated. The end effect is that groups or persons are cast into subaltern positions.
So you see, it has to do with socio-spatial relations, and scriptive processes and practices, and subaltern position acquisition through passive-voice casting.
My advice is to ask your teacher or professor what "discursive violence" means. I'm sure he or she has some definite ideas on the subject—and from a practical perspective, those ideas are what matter most.