Dear Paula,
Your question reads like you want the entire tree removed.  The easiest way to do that is to dig it out which would include taking the suckers out as well.  You would be able to see the and dig out the roots as well.

Do you just want to remove the suckers? Then you would dig down on the side of the tree a good foot maybe more and take them out with the root.  You can cut the suckers on the trunk above the soil at the trunk, make it a clean, sharp cut, do not tear the trunk.

If you do want to take the whole tree out, you can cut it down or hire an arborist to do it and then have them take a power blade to the stump and turn it into wood chips.  That usually kills the tree and the roots.  There are also solutions to purchase that you put in a hole in the stump.  That will kill what's left of the tree but it does take a year or so.

You may have some growth come up after the tree is out if some of the roots are left.  You need to check on it periodically and dig them out.

I have attached a link about removing suckers: https://yardandgarden.extension.iastate.edu/how-to/managing-suckers-fruit-ornamental-and-shade-trees

If you have further questions, please contact us again.