I believe this is a gall caused by the bacterium Agrobacterium tumefaciens commonly referred to as crown gall mite or possibly Plum Bud Gall Mite (Acalitus phloeocoptes (Nalepa)). Crown gall, as its name implies, typically appears at the crown of a plant, where the trunk enters the soil but it also can infect the main trunk and side branches. Plum trees are among a long list of plants commonly
infected by crown gall including many popular home garden fruit trees.

When cut with a knife, crown galls are softer than normal wood and lack the typical pattern of annual growth rings. Galls can be tiny and smooth on young
plants but usually are rough and sometimes massive on older trees. On plum trees, the gnarls will be soft and sometimes hollow. The galls stunt the growth on young trees and can cause wood rot on older trees.

Galls are abnormal growths that occur on leaves, twigs, roots, or flowers of many plants. Most galls are caused by irritation and/or stimulation of plant cells due to feeding or egg-laying by insects such as aphids, midges, wasps, or mites. In the case of crown galls, however, the infection is the result of infections by bacteria, fungi, or nematodes.  Because crown gall is bacterial, it is particularly problematic because it can live independently in soil and in roots. This means that even if you get rid of a diseased tree, the crown gall can remain.

Affected trees ordinarily show little injury, although foliage of young trees is sometimes completely deformed. On ornamental trees this condition can be unsightly. If you have only a few of these and they are on smaller limbs, you can remove the affected limbs back to the main trunk, thereby removing the gall. This may help prevent further occurrences. Although unsightly, you may wish to just leave the galls alone, especially if your tree is older. There no effective treatments for Crown Gall, but some botanists suggest just tolerating it for the life of the tree. Trees can continue to bear fruit.