I bought the Uno with the long pins on the back by mistake. With the pins, my board won't mount where I need it to. Is it possible to cut them down or would this damage anything?
Show us a good image of what you bought.
Sure, just cut one at a time to keep shock levels down, and do not let conductive debris remain on the Uno.
I believe this is the product:
You need what is known as a side cutter to remove the pins close to the board.
And don't let them fly off at someone, they have considerable velocity.
Also, wear eye-protection (if no eye protection) - just in case.