Cut them off a foot or so above ground, then immediately paint the cut surface of the stump with a weedkiller. Most effective are products labeled woody plant killers which contain 2,4-D and/or triclopyr. One available around here is Blackberry and Brush Killer.

You'll most likely have to re-treat one or several times. Each time, make a new fresh cut on the stump.

vinegar on the stump, I used it to killl the 'dreaded lilac' THAT WAS THREATENING TO TAKE OVER MY YARD, IT ALREADY HAD IT'S OWN ZIPCODE! I cut it to ground level, chopped the roots all around and poured vinegar on it, then a backhoe operator kindly popped it outta the ground for me, I also covered it for many days with a tarp to heat it up, keep water off of it, to kill it faster, vinegar kills weeds without killing the environment.

PL