Those little sprouts eventually become the trees that form a Live Oak Motte.
They either come from acorns or sprout directly from the roots. What Kenneth said is true, Round Up doesn't have residual life in the soil, but it is highly likely that the sprouts you are seeing stem directly from the parent trees you have trimmed up (and I assume would like to keep).
In this instance the herbicide you spray will directly damage the parent tree. It is also likely that someone on this board has sprayed these same time of shoots with Round Up & no doubt had amazing results. If the shoots are small, they may not absorb much Round Up to cause severe damage to the parent tree. Key word being may. These large trees take a long time to die & many have been weakened by the drought of the last four years. Your spray could be the proverbial straw that breaks the camel's back which allows Hypoxylon Canker or some other disease to overwhelm the Oak's natural defenses & kill them.
TL, DNR version: Round Up will hurt the oaks to some degree & may kill them. Get a goat or a grubbing hoe.
