This title is referred to in David Crouch's The English Aristocracy, 1070-1272: A Social Transformation, (New Haven and London, 2011), 188. This anonymous reaper-reeve was outlawed for his participation in the brutal torture and murder of a teenage boy, Robert Palmer. I've never come across this title before and Google is only throwing up fantasy books. Has anyone come across this position and know what duties they might have had?
I find a few citations in Maitland which refers to 'the reaper' and 'the reeve' in one sentence for late middle ages, which suggests that hyphenated titles mean a person is both. Maitland also refers several times to someone who 'acts as a reeve', which suggests that 'reeve' was an office/title, but not necessarily a full-time job.
Crouch in another work (in an index) puts beside this name the latin messor, which in latin is a harvester, mower, reaper of crops.
So, I think it's not a title but instead a hyphenated descriptor invented by historians.