We introduce a new type of optical isolator based on breaking time reversal symmetry in dissipative finite Su-Schrieffer-Heeger (SSH) waveguide arrays that support topological edge states at one end of the structure. In the forward propagation direction, light is launched into the edge waveguide to excite the localized topological midgap state. As a result, most of the input optical power is transmitted to the output port. On the other hand, backward reflected light encounters a propagation constant mismatch in that same channel which shifts the otherwise midgap state into one of the bands and hence becomes delocalized over the whole array. We show that under these conditions, a judicious spatial distribution of the optical dissipation across the structure can produce an isolation ratio of -50 dB. The required nonreciprocal phase shift is introduced by depositing a magnetic garnet film only on the edge waveguide and, thus, the required magnetic field can be generated by an integrated micromagnet. Similar concepts can also be applied to SSH arrays made from optical resonators.