If you are talking about using the filter in a report, reports can be saved with the filter intact. See the "save this report" button on the button bar.
If you are talking about the use of the filter at the bottom of the index in the Family page, or in exporting people; no, you can't save it.
But, if it is a complicated, mulit-step, filter, you can create the data set and then create a custom fact to use to record a "tag", or a text string, that you can filter on in one step.
I do that with my military veterans. I have a Military Filter custom fact that shows:
War - Which side (if not evident) - family line(s) - survived or not.
Civil War Union Jones Casualty
Civil War Confederate Jones Survived
Civil War Union Smith Survived
World War II Williams Smith Jones Casualty
With this tag, I can pull out all of my Smith's that died in the Civil War, or died in any war, or all of my lines that participated on the union side in the Civil War, etc. etc.
Unfortunately, you can add that fact to each person in a person's family or one person at a time - but you can't assign "tags" en masse.