Desert Willow Cut Down Advice

If my gardener cut down my five-foot-tall desert willow (looked like a stick in the ground, down to 2 inches) will it survive or does it need to be replaced? The roots are good and have two leaves at the base.

Do you mean it's a dead top above the leaves? Normal tree surgery/pruning would be to cut above the live growth, possibly at an angle to shed water. Willow will usually sprout again from the roots. Before digging it up, I would see what it does this year.