Many of the most popular garden trees are grafted on to rootstocks. Flowering cherry, flowering crab-apple, flowering hawthorn, mountain ash and whitebeam are examples. Any of these might produce suckers at ground level or at the top of the trunk – wherever the graft union is located.
Strong upright shoots may be coming from the rootstock
Suckers usually have small or coarse leaves and are more vigorous than the grafted variety. The young shoots should be removed as soon as they are noticed, or they will take over. They can be pulled or cut away, or chop them away with a spade if they are below soil. Firm the ground well to discourage further suckering.
A few other plants, although not grafted, produce suckers, for example stagshorn sumach, poplar, kerria and snowberry. These suckers arise from the roots of the tree or shrub and are the same plant.
If they arise from trees such as stagshorn sumach or poplar, they should be removed. If they arise from shrubs that naturally spread outwards by suckering, such as kerria or snowberry, they can be left in place if they are not a nuisance.