How do I get rid of all roots of an old Acacia tree that was cut down?

We cut down a large Acacia tree and then had the stump removed. Once we did that, we thought that would kill off all the suckers that were popping up. But a few have started to come up again. I think the roots are growing to close to the house and mighting be too close to the sewer/water lines with possibilty of the pipes breaking. I tried pulling up the foliage hoping to take the root but it's very had to do. Any idea of getting rid of this pesty tree once and for all?