Jim and J.R. above are right.
In vulgar slang, the verb "blow" literally means "to perform oral sex on (a male, or the male sex organ)", and like other verbs with that meaning (such as "suck"), it has come to used figuratively as a term of abuse meaning roughly "to be terrible". (In origin I assume it's intended as a homophobic slur — "he blows" → "he performs oral sex on men" → "he's gay" → "I am hereby insulting him" — but it's commonly used for any variety of things. The same, for that matter, is true of "be gay"; "School is gay" would also be an expression of disdain for school.)
"Blows dogs" takes this further, since it would literally mean "to perform oral sex on male dogs", but it's still just a way of saying "is terrible". I think the original intent is to make the insult more vivid, since "blow" had lost all of its metaphorical force and much of its "shock value" (its ability to surprise the listener and evoke the desired extreme emotion). Changing "blow" to "blow dogs" re-emphasizes the literal meaning, and also makes the literal meaning much more extreme, so it restores some of the shock value.