Depending on certain factors, you'll either want to do this with a before commit Event Handler (if you want to make sure it's <always> updated), or add it to your save microflow after any changes to the source attribute are made (for instance, if you only want it to be updated when the attribute is changed in a single place). 

Either way, in your flow, make sure you have the $Object you want to change, then use a change object activity where you fill the new attribute with substring($Object/SourceAttribute, find($Object/SourceAttribute, ‘-’) + 1) or something similar, depending on whether you need stuff after the dash or before it.