The ability to reverse protein aggregation is vital to cells. Hsp100 disaggregases such as ClpB and Hsp104 are proposed to catalyse this reaction by translocating polypeptide loops through their central pore. This model of disaggregation is appealing, as it could explain how polypeptides entangled within aggregates can be extracted and subsequently refolded with the assistance of Hsp70. However, the model is also controversial, as the necessary motor activity has not been identified and recent findings indicate non-processive mechanisms such as entropic pulling or Brownian ratcheting. How loop formation would be accomplished is also obscure. Indeed, cryo-electron microscopy studies consistently show single polypeptide strands in the Hsp100 pore. Here, by following individual ClpB-substrate complexes in real time, we unambiguously demonstrate processive translocation of looped polypeptides. We integrate optical tweezers with fluorescent-particle tracking to show that ClpB translocates both arms of the loop simultaneously and switches to single-arm translocation when encountering obstacles. ClpB is notably powerful and rapid; it exerts forces of more than 50 pN at speeds of more than 500 residues per second in bursts of up to 28 residues. Remarkably, substrates refold while exiting the pore, analogous to co-translational folding. Our findings have implications for protein-processing phenomena including ubiquitin-mediated remodelling by Cdc48 (or its mammalian orthologue p97) and degradation by the 26S proteasome.