This looks like black knot disease, a fungal disease caused by the pathogen Dibotryon morbosum. This is a fairly common disease of plum trees, although some varieties are more susceptible than others. Recommended treatment for this disease is to prune the affected branches off the tree about 6 inches below the gall (the swelling on the branch) and to remove these branches from your property. (The galls can release fungal spores if they are kept on the property and can reinfect the trees.) The good news is that this is not a systemic disease – the entire tree is not affected, just the branches with the growths. But if many of the branches of your tree are infected you may have to remove a large enough number of them that the tree’s health will be compromised, and in many cases homeowners (and orchardists) have to remove entire trees if the infection is extensive. Here is some additional information about this disease.

https://ecommons.cornell.edu/bitstream/handle/1813/43075/black-knot-plum-FS-NYSIPM.pdf?sequence=1

https://www.extension.umn.edu/garden/yard-garden/trees-shrubs/black-knot/

http://msue.anr.msu.edu/news/your_plum_trees_versus_black_knot

Hope this helps.