Side garden back-o-tricks

I was just mulling over how to attack the out of control cactus we have in the side garden, and saw a spiny and angry looking vine. Curse you garden, more friggin fruit?! Now I gotta worry about raspberries?! I tried to figure out where they were even growing from, and I think they snuck in from between the third fig tree and this condominium of a cactus.