When using "Save As" which saves your new version, you have three optional things you can do: (1) and replace ...,(2)and append to end of set ..., (3)as a new independent problem. The first replaces the original version by the new version in the student's assignment. The second keeps the original version in the assignment and also adds the new problem to the end of the assignment. I think the third is just the default action, which saves the problem but does not assign it to students. You can then use the Hmwk Sets Editor to assign the problem if you want.
Arnie