It has recently been shown that torsion can break liquid bridges of viscoelastic fluids, with potential application to their clean and rapid dispensing [Proc. Natl. Acad. Sci. U.S.A. 118, 24 (2021)]. However, many commonplace fluids (paints, adhesives, pastes, and foodstuffs like chocolate) have more complex thixotropic elastoviscoplastic (TEVP) properties that depend on the imposed stress and the timescale of deformation. Using a commercial thermal paste, we show that liquid bridges of TEVP fluids can also be broken by torsion, demonstrating the applicability of the technique for improved dispensing of real industrial fluids. The liquid bridge breaking mechanism is an elastic instability known as “edge fracture’. Dimensional analysis predicts that the effects of thixotropy and plasticity can be neglected during edge fracture. Simulation using a nonlinear, phenomenological TEVP constitutive model confirms such a prediction. Our work yields new insight into the free-surface flows of TEVP fluids, which may be important to processes such as electronic packaging, additive manufacturing, and food engineering.