If they're being actively insulting - using foul language and clearly just commenting to be mean and disruptive ("This is shit", "Why do you suck so much", etc., etc.) - then I delete the comment if I can, and never respond. There is no response that would make them, or me, happy, so ignoring it is the only way to go. The same goes for people who are being actively creepy, though luckily, I haven't had any of those.
If it's just a negative comment, I let it stand - not everyone is going to love my comic, and they have as much right to express that as anyone else. As long as they aren't being disruptive or trollish, I leave them be.
And if I get a harshly worded critique, I respond to it and ask for further detail; if someone has gone through the trouble of typing up something long enough to qualify as a proper critique, the least I can do is respond and try to analyze what they've written; they might have spotted genuine flaws in my work that I can improve upon.
But the general rule of thumb is to not engage with hateful comments; delete and ignore, because there is no fight there that you can possibly win. They just want to spew hate.