If you want to be sure that there is no Tiffany left let it bloom this year and see. Some of those leaves in the center don't look like Huey to me. If you do get some Tiffany blooms you'll know which canes are good and which ones to rip out. Rip is the key word. Don't just prune it off because it will return. You need to damage the cells so they won't send out new growth. Dig down below the soil to where the cane come off the roots and rip it off there. That should prevent it from returning.

If you don't want to bother and would rather just start fresh I would cut it all off just above the soil and then digging it out should be easier.