Getting rid of a nuisance Poplar tree

If there is a thread for this please help direct me there, if not;
Here's the problem I have three poplars in a clump, they are lifting the cement pad of our garage and the suckering roots have traveled 25-30 ft from the stumps.  I need these trees and the suckers gone for good.  I have a very tiny city lot and they have made growing in my front yard nearly impossible. I have managed to dig many of the long long roots out but I know I cannot find them all.   I cut them to the ground this summer and used the logs for hugelkultur and mushroom growing in the past.  I tried to embrace this clump as my biomass supply but I need to expand the garage into a living space next summer, I really want the trees gone.  HELP!  I really do not want to use diesel and stump killers  

Since your lot is tiny and you have mowed them down, the only thing that I can think of to do, is to keep mowing them down, or perhaps better strip them of their leaves, which causes the tree to loose a lot of moisture and forces it to use growth potential.  Do whatever you can to eliminate the potential of the roots to continue to grow.  Over time, no tree can handle consistent mowing or de-leafing.   vigilance and perseverance will pay off, but it will take both.

I suppose I suspected that, I think I will hire a stump grinder and remove it physically.  Then as you suggest stay on top of the suckering roots. I need to put a foundation there and repair the damage done.  I have to hope and figure once the foundation is poured the light will be blocked.  Thank You Roberto.

If you are not killing with chemicals or salts most poplars can be incredibly determined.  You should specify type of poplar.

Hybrid poplars and cottonwods are not prone to suckering as long as you do NOT disturb the soil ie cut the roots.  These trees can be killed off by girding the trunk and destroying the few suckers.  Girding is best done just after the leaves are out in the spring as they seem to be less inclined to try and sucker.   Be aware it takes at least 2 full years(possibly 3) before you can disturb the roots without getting suckers everywhere you cut a root.  Every time you cut a root if it is not attached to a growing tree it will try to make one.   You can chop a root in 20 pieces and get at least 20 suckers starting off that root. Cottonwoods can also be killed by 5 to 6 months of continous immersion in water.  They like it short term and will actually look healthier but after months of the roots all being under water they begin to die.

Aspen sucker like crazy with no soil disturbance.  Kill the main tree, dig as many roots as you can and then mow everything for a number of years.

Other types of poplar I have no experience with.

It is a hybrid poplar from what I can tell, very large leaves .. When we bought the house it had been ground down below soil level and left covered with the chips.  Over the last 9 years we allowed it to grow back and had to reduce the height a few times. When it came time to shorten it this year I did a lot of inspection since it was causing problems.  I had them cut all the way down to the ground mid summer so I am stuck with that decision and history.  I have pulled out super long roots for years out of my beds out there, by severing them and digging the entire length. So now I have self watering tanks  using stock tanks for the growies out there so the roots won't keep traveling there. (video link below is to self watering bed inspiration)  ANYWAY..  So I have droughted it and will scalp it.  I will miss the wood for mushroom growing, and wish I could inoculate the stump but it is in full sun .. so.  Anyway I guess I just wanted to hear that I was right in my suspicion that this IS a difficult tree to have (or remove) in the wrong spot.  This was my solution to keep the water use out front to a bare minimum and it did work for us, I plan to build quite a few more with this principle. Thanks for you reply C. Letellier!