Roots from woody brush/saplings

After cutting woody brush.saplings with a pruner or machete, should I completely dig out the roots? Someone told me that it is ok to leave the stems from out of the ground, and that mowing and time will eventually kill off the roots. Doesn't sound right.
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i think that leaving them and mowing will eventually kill them, does around here. lucas
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I did the same thing as you...they never went away..they keep coming back. I can't remove the roots cause there's just to darn many.
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