1865 US 2 Cent Blank Reverse.

to be positively sure. There is no way a coin would only be struck on one side with a collar, there is a chance it could have two blank planchets fed into the coining press making a capped (one sided) struck coin, but usually this leaves a reversed or mirrored impression on the blank side. True errors in the Two Cent series are very, very rare for some reason. even with 1864 and 1865 high mintage's there are only a handful of known errors like off centered, capped dies or double strikes. I've been tracking errors in this series fro several decades, and can say Ive seen less than 3 capped dies, 6 off center pieces, and 2 double struck Two Cent Pieces.

Looks to be ground down on the reverse side. Can you get a weight of the coin to the nearest tenth of a gram, a Two Cent Piece should weigh 6.2 grams. How about a photo of the edge on, to see if it is as thick as a normal one. Is it even in thickness all the way around?

I'm pretty positive this was done after leaving the mint.

Yep from the look of that rim it's a shave job. Too light and the weird lip on the rim is a give away, looks like a start of a "love token" where one side of a coin is shaved off to make it smooth, then an engraving - usually initials are carved onto the smooth side along with scrolls, flowers, etc.