We cut down a 30 foot volunteer poplar in our yard that the idiot previous owners had allowed to grow in a bad spot - cut it down, ground out the stump, and just kept digging up the shoots that popped up. It’s done for good now (she says, tempting fate). It was beside a lilac, and maybe that helped - lilacs are bad-ass. 
I’ve done this with Alianthus trees (tree-of-heaven), they look like Sumacs. They send out shoots from the roots when you cut them down too. I’ve soaked the leaves with Roundup, you can also cut into the trunk and spray some Roundup in there too. Cut it down when all the leaves turn brown. Then check it every spring, just in case it rises from the dead.