I was able to use GED file software, The Complete Geneology Reporter, to create a report that lists unconnected people (relative to the primary person). It lists unconnected individuals and unconnected sections (islands).
Then, referencing the report I could manually delete the people from my ancestry.com tree. A handy feature in Ancestry.com is "View Relationship to me". I check there to make sure there isn't a relationship before I delete.
I also used the family view of an unconnected section to prune the sub-tree.