Cut off each one as it sprouts and immediately paint the cut surface with a weedkiller for woody plants, the active ingredient either 2,4-D or triclopyr.

If you keep the leaves cut off so they cannot use sunlight to photosynthesize and manufacture nutrients that the roots store so they can send up new growth the plant will die off and there would be no reason to spray, or otherwise apply, a poison around your yard to pollute your environment.
Since most plants have a very thin cambium layer to move nutrients up and down the stem to the roots and leaves the most effective method of apllying these plant killing poisons is on the leaves where they are absorbed and moved down to the roots which then kill the roots. Painting a stem that is less then 1/4 inch in diameter is not easy.

Probably a morus (mulberry.)

I would go with paper mulberry, Broussonetia papyrifera. Probably coming back from root suckers.
hortster

Here is a link that might be useful: Paper mulberry

Link to paper mulberry.

Here is a link that might be useful: Paper mulberry