I ordered a bulk quantity of components for experimentation and they were shipped in a cut tape format.
I've been removing components individually from the tape but it requires a large amount of labor, removal of tape residue from the leads, etc.
Is there a better method?
The top tape should just peel back, and should allow you to dump the components on the table. I have never heard of tape residue on the leads.
If there is such residue, you could either bathe them in an electronic cleaning solution (3M Novec comes to mind) or just cut the residue parts off, if the leads are long enough.
EDIT: I just realized you are talking about through hole components. Most of the time, I have never needed to clean them, as we cut the leads after they are soldered into the board, and you can just let the residue part be. An easy way to prep the components is when you are about to solder, apply some flux from a flux pen, and that should clean the surface so that you can solder it. 3M Novec would also work too on this as well.
For reference to others, this is what I believe that you are referring to.