A thermally curable pressure-sensitive structural tape (SAT-0) was prepared using an epoxy acrylate copolymer and an epoxy resin and modified with a wollastonite microfiller (SAT-W) and a halloysite nanofiller (SAT-H). Influence of the minerals on self-adhesive features and curing behavior of the tapes as well as on shear strength of aluminum/SAT/aluminum joints has been investigated. Thermally uncured SATs containing the fillers exhibited higher Tg (+5 °C for SAT-H), adhesion (+64% for SAT-H) and tack (+10% for SAT-W) while their cohesion was lower (−22% for SAT-W and −86% for SAT-H) in relation to SAT-0. Moreover, filler addition reduced the shear strength of the Al/SAT/Al overlap joints (−6% for Al/SAT-H/Al and −22% for Al/SAT-W/Al), however, the microfiller-based systems exhibited better crack and fatigue resistance, and higher shear strength after ageing tests than SAT-0 and SAT-H (+100% after thermal ageing, +85% after exposure in a climatic chamber, and +27% after immersion in a fuel).