Yes, it would have the potential to translocate into main tree. How devastating this would be I can't say. You could use a "burn-down" type of herbicide though with no such worries, these materials simply killing whatever portion of a given plant they come in contact with, but not being systemic. Diquat, paraquat, and some salts of fatty acids types, ie. "Sharpshooter" might work for you, without fear of harming mother trees. The challenge then would be to not kill surrounding turf, if I'm understanding you correctly that these suckers are happening in the lawn. Otherwise, just let your lawn mower take care of them. The trouble with such suckers is that the more you do to the tree to try and stop them, the more determined the tree becomes to make new ones. As light an approach as possible.

+oM

thats what a poplar does ...

and when it increases.. it MIGHT mean.. the mother tree is in decline ...

it would be nice to fully ID what kind of poplar ... and how big it is ...

many are very short lived.. in tree terms... and a rather weak and brittle tree ... and when they start to fail.. they can drop very large chunks of tree ... so the issue becomes ... will it wall on you or your house... or a neighbors ..

i would bet.. at planting .... this is one of those tree decisions.. where someone wanted a fast growing tree ... and then moved.. before it became a fast dying and problematic tree...

we need the ID.. and a couple pix.. to see the situation ...

ken

Here's the poplar (cottonwood). Probably 100' tall, or close to it. The problem isn't so much coming up in the lawn (I do mow over them), but in planting beds where I have perennials growing and, as I noted above, coming up in my gravel driveway. Click image to get full view.

Yup, I feel your pain, having battled suckers from another tree type in garden beds for some decades now. I clip mine, maybe twice per summer, for the most part. It seems too that tearing or plucking them out-when able to do so-works better than making nice neat cuts with hand pruners. That's mostly if you get to them in time. Once they get rough and tough and woody, they won't twist off anymore. Also, timing seems to make some difference. So, on my trees-a cultivar of choke cherry BTW-I have to go after them in early summer or they'll take over the garden beds. But then, if one can get the next round about mid-summer, there's usually not much regrowth after that. Until the next year of course!

That's all I've got. Don't let anybody talk you into landscape fabric as a cure for this issue. It not only won't stop them, but now they will be half under the fabric, half growing above it. That's a real treat to deal with!

+oM