Although Grackles aren't Corvids (crows, jays, magpies; generally considered to be among the most intelligent birds) they're still very smart. Knocking down the nest would freak them out and probably cause them to leave.

It's a different situation if they're just using the tree to roost, and you'll probably have to kill one or two to get it to end.

In that case, I'd recommend a quiet, accurate pellet gun. Consider the Daisy Powerline 880 (variable power pump, relatively quiet) or pellet guns from the Gamo Whisper line (break-barrel and significantly more powerful, although perhaps a bit louder). Don't waste money on the super-deluxe plastic-tipped or gold-plated pellets. Standard lead pellets are plenty accurate and, if fired from either of those pellet guns, will have more than enough energy to completely penetrate a bird. Also, avoid BB guns (Red Ryder) or smoothbore pellet guns (Crosman Pumpmaster 760) - they lack the kind of accuracy you'll want - and avoid shooting BBs down the barrel of your pellet rifle (they fit more loosely than a pellet and, over time, will bounce around and damage the barrel's rifling).

Whatever you do, get your gun sighted in before you start taking shots at birds. There are plenty of people on CB that would be happy to provide tips about that if you need help with that.