Elm Tree cut down and now many saplings... Help please!!

I had a very large elm in my back yard that each year would lose huge branches and was turning black. Found out that the squirrels had hollowed it and it was dieing. We had a company come out and cut it down and now I have so many saplings growing throughout my yard, all over the place.(and the tree company left a partial stump) Is there any way of killing this tree for good? Any suggestions would help. Thank you
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