Where do I cut glued piping to reconnect a new p drain for new sink?
You've got two choices: right below that threaded piece on the vertical run or the backside of the 45 degree bend close to the wall. the second choice is probably the one you'll need. Cut right at the edge of the bend with a hacksaw and stay as close to the bend as possible, You'll want to save as much of the pipe coming out of the wall as possible for your new connections. You can then use those "screw this nut" connections for the new drain.

With those screw is nut connections, assemble all the pipes and only slightly tighten. Once they're all together, go back and really tighten them up. The directions say only hand tighten but I have always had to give them an extra eighth of a turn with a pair of channellocks.