Remove the remaining cucumbers from the bush if you desire.
Grasp the vine at the soil level and slowly pull upwards to remove the roots along with the vine. Depending on the size of the vines, and the depth of the roots, use a hand shovel to help dig out the roots if they do not come up with ease.
Place the vines into a trash bag and tie the bag up.
Dispose of the trash bag away from other vegetable plants to ensure pests and any possible diseases that the cucumber plant may have carried will not spread.