Reducing fibrous aggregates of protein tau is a possible strategy for halting progression of Alzheimer's disease (AD). Previously we found that in vitro the D-peptide D-TLKIVWC disassembles tau fibrils from AD brains (AD-tau) into benign segments with no energy source present beyond ambient thermal agitation. This disassembly by a short peptide was unexpected, given that AD-tau is sufficiently stable to withstand disassembly in boiling SDS detergent. To consider D peptide-mediated disassembly as a potential therapeutic for AD, it is essential to understand the mechanism and energy source of the disassembly action. We find assembly of D-peptides into amyloid-like fibrils is essential for tau fibril disassembly. Cryo-EM and atomic force microscopy reveal that these D-peptide fibrils have a right-handed twist and embrace tau fibrils which have a left-handed twist. In binding to the AD-tau fibril, the oppositely twisted D-peptide fibril produces a strain, which is relieved by disassembly of both fibrils. This strain-relief mechanism appears to operate in other examples of amyloid fibril disassembly and provides a new direction for the development of first-in-class therapeutics for amyloid diseases.