Depends on the .177 caliber gun we're talking about. Something like a Daisy Red Ryder probably couldn't kill anything bigger than a garter snake. Something like a RWS 34, Benjamin Discovery, RWS 350... could kill a good sized snake if you hit something vital (brain or spine). However that's a lot of ifs to worry about if you have to deal with a venomous snake.
Honestly I think if I had to deal with a venomous snake (or any snake really), I'd much prefer a shotgun. The reason is actually really simple. A .177 caliber pellet gun will basically punch a small hole through the snake. Unless you get very lucky and hit either the brain or the spine, the snake isn't going to die immediately. Which means you have to reload and shoot it again. And again. And again all the while hoping the sucker finally bleeds out. And the snake won't be sitting still while you do that. It will either try to slither away or strike at you. A shotgun on the other hand, even a .410 using .5 ounce, 2.5-inch loads at the 10 feet or so you're likely to be shooting at will kill a snake with the first shot every time, provided you manage hit the snake. If for example you aim for the head, the snake basically won't have a head left. And this is with a diminutive .410 shotgun shell... A typical 12 gauge field load delivers 1.25 ounces of shot. It literally will blow most snakes (except for something like a big python, anaconda, or a huge rattlesnake) in half. And provided you hit the snake a 12 gauge is going to deliver a 1-shot kill every time even on a huge snake. Since that's the case, the odds of an injured (and aggressive) snake getting away are greatly decreased. Ditto on you getting bit while you try to kill the snake. And that's a very good thing.
As for what else a .177 caliber airgun can kill... Again it depends on the gun. However assuming you're asking about one of the "adult" airguns that produce 12-15 ft-lbs of muzzle, energy, you can add nuisance birds (English sparrows, starlings, feral pigeons) and rabbits to the list. Ditto on frogs, chipmunks, iguanas, and other animals in that size range. However, in spite of Gamo's marketing claims, larger animals like raccoon, fox, etc... are too large to reliably take with any .177 caliber airgun.