This problem arises every deer-hunting season, when folks who shhot oinly once a year get confused and load their rifles with the wrong ammunition (say, .280 Remington in a 30-06). You should make it a habit to carry ONLY the correct ammunition for the firearm you are currently using.
Your question about how to dispose of unwanted ammunition is really an excellent one- NEVER discard it in the trash, or into a dumpster or landfill. I recommend taking it to your friendly local gunstore , and asking the proprietor to dispose of it for you (or sell it, whichever comes first!) Do not attempt to remove the bullets from the cartidges using household tools in order to render the ammunition "safe"- this will almost guarantee a bad accident- and I have seen a few of those. By the same token, burning it is extremely hazardous to everyone in the vicinity.
I once saw an M-1 rifle from which someone had attempted to fire a rifle grenade- but used a regular 30-06 cartridge rather than a blank. Pretty impressive- I think that qualified as a "bore obstruction", all right!