The way to delete groups of people in FTM is through selecting groups of individuals in charts in the Publish Workspace. I know, it sounds like an unlikely place to put that capability. I guess they put the delete capability in an unlikely place to make it harder to do and thus harder to delete people by mistake. Who knows?
Once you have found a chart that gives you the dataset you are looking for, likely an ancestral chart, you right click in a blank area of the chart and choose to Delete > Everyone in the chart.
I would make a backup of your old file to keep for reference.
One thing to look out for is peripheral relatives. Multiple spouses of ancestors won't be included in an ancestral chart, nor will siblings of ancestors, children from previous marriage, children of other spouses of ancestors from their other spouses, etc.
To get all peripheral relatives, you might want to:
1) Detach your "undesired ancestral group" from your desirable group. This would probably entail Person > Detach > Detach from a family where he / she is a father/mother of a family.
2) Select a person in the "undesirable ancestral group" and run the Extended Family Chart.
3) Uncheck "All individuals".
4) Run it for a desired number of generations.
This chart will (should!) pickup all of the peripheral relatives in the "undesired" bunch, that a straight ancestral chart might miss. Then you can right-click > Delete.
Another thing you might want to do is to keep the dataset of what you are deleting in a separate file. You can export the records you are deleting - before deletion - in the same manner. Get them all in a chart, Right Click Export. Then Right Click Delete.