Are the offending willows seedlings or suckers growing from the roots of established trees or thickets?
Seedlings can be killed eventually by mowing but only if mowing is frequent, persistent, and done soon after germination.
Suckers will grow from established roots so long as the parent plant remains or until energy stored in the root system of its stump is exhausted. For best results apply a "brush killer" in early summer or a non-selective herbicide in the fall to the freshly cut stumps of parent plants. Do the same to cut surfaces of suckers so long as they persist. Chemicals applied only to suckers may affect the health of parent plants, so don't use chemicals on them if you value the parent plants.
Here are links to more information:
Cut Stump Application of Herbicides
Chemical Control for Woody Plants, Stumps and Trees
