no you don't need to cut anything.. all you need to do is match the wires FROM the aftermarket radio TO the wires on the harness adapter and cover them with electrical tape, THEN you plug the adapter to the Toyota harness that unplugs FROM the back of your radio and you're done. That's it.
If you don't wanna do any matching, you can spend a few more dollars and go for specific brand to car adaptors.. you can get Kenwood to Toyota, JVC to Toyota, Sony to Toyota, etc.. then all you do is plug one side on the Toyota harness, and the other side on your stereo and done.