AAA+ proteases and remodeling machines couple hydrolysis of ATP to mechanical unfolding and translocation of proteins following recognition of sequence tags called degrons. Here, we use single-molecule optical trapping to determine the mechanochemistry of two AAA+ proteases, Escherichia coli ClpXP and ClpAP, as they unfold and translocate substrates containing multiple copies of the titinI27 domain during degradation initiated from the N terminus. Previous studies characterized degradation of related substrates with C-terminal degrons. We find that ClpXP and ClpAP unfold the wild-type titinI27 domain and a destabilized variant far more rapidly when pulling from the N terminus, whereas translocation speed is reduced only modestly in the N-to-C direction. These measurements establish the role of directionality in mechanical protein degradation, show that degron placement can change whether unfolding or translocation is rate limiting, and establish that one or a few power strokes are sufficient to unfold some protein domains.