1.0 Make (something bad) less severe, serious, or painful:
1.1 Lessen the gravity of (an offence or mistake):
The etymology suggests softening action:
early 15c., "relieve (pain),"
from Latin mitigatus, past participle of mitigare "soften, make
tender, ripen, mellow, tame," figuratively, "make mild or gentle,
ultimately from mitis "gentle, soft"
(from PIE *mei- "mild") + root of agere "do, make, act" (see act).
First element is from PIE root *mei- "soft, mild."
1.0 Appease the anger or anxiety of (someone):
1.1 rare Reduce the severity of (something):
The etymology suggests to make soft:
late 14c., "to soften (a substance),"
from Old French mollifier or directly from Late Latin mollificare
"make soft, mollify"
from mollificus "softening,"
from Latin mollis "soft" (see melt (v.))
+ root of facere "to make" (see factitious).
Transferred sense of "soften in temper, appease, pacify" is recorded
from early 15c.
Related: Mollified; mollifying.
In definition and connotation, these two words share a lot in common, but from the 16th century forward, the word mitigate has been applied more commonly to circumstances, while mollify has been applied more commonly to hearts and minds.