When I discovered a thinner tape with adequate holding ability that was easier to remove, called XFasten Double Sided Tape, I started using it instead of turner's tape. The down side was that this tape cut poorly with scissors, and the backing tended to separate prematurely when small pieces were needed.
The solution was quite simple: attach an end of the tape to the workpiece, unroll the amount needed and press it down, then cut the tape with a razor knife. The wood stabilizes the tape, but you need to be careful not to score the wood as you cut.
