saplings in privet hedge

Let the stubs start to leaf out a bit then paint the leaves with Roundup. Use a small brush and do not get Roundup on the other plants. You may have to do this several times, but you should be able to kill the offenders off.

This all assumes that simply pulling the saplings out hasn't worked. Some plants just need a bit of root in the ground to take off again.

Charlie

You can cut them down, but, as you've discovered, there's still a lot of biological material below ground.

There's any number of things you can paint the stumps with, but I've found that covering the stump with a coffee can works.

If you dring Folger's decaffeinated that comes in the green plastic container, the can might even be unnoticeable.

I've used roundup to kill small saplings in the same situation. Cut them to the ground and when they sprout a few new leaves, paint or spray carefully with roundup. It may take two or three tries, but killing the leaves will eventually kill the sapling. Much easier than trying to dig them out. Digging down a little bit, and cutting off below ground might also work.

A few drops of 25% Roundup (glyphosate) applied to the stump immediately after cutting will take care of most any woody plant.