removal of sumac (possibly stagshead) suckers

hello fellow gardeners, my neighbour has recently cut down his sumac tree hooray! i currently have about 80 suckers coming up in my garden. while my neighbour remained happy with his sumac i just pulled the suckers out constantly. but now the tree is thankfully gone i want to eradicate the runners. they are in the lawn and border, what would be the easiest way of doing this please. thanks

 

Didn't know what a sumac tree was, so googled and found this. Thought it might be helpful:

How to manage invasive sumach trees & root suckers

 

Crocus, by cutting down his tree your neighbour will create loads more suckers. Pruning, cutting, etc promotes lots of root activity....it is a survivor.
I would use a lawn weedkiller on the sprouts in the lawn; for the border I would use glyphosate. As JWK said, it is a big job!
A neighbour here, luckily far away from me, has a few Sumachs...he loves 'em but is no gardener. I can see no reduction of suckers in his grass. The mower cuts them but more and more appear.
I was fortunate...when I first started planting things a friend warned me about my newly planted Sumach. It was whipped out there and then.
Invasive plants should have a warning on them

 

thankyou for your helpful reply's, i will prepare to do battle with these suckers, whoops nearly typed something else.