Twisted interfaces between stacked van der Waals (vdW) cuprate crystals present a platform for engineering superconducting order parameters by adjusting stacking angles. Using a cryogenic assembly technique, we construct twisted vdW Josephson junctions (JJs) at atomically sharp interfaces between Bi ₂ Sr ₂ CaCu ₂ O _{8+ x} crystals, with quality approaching the limit set by intrinsic JJs. Near 45° twist angle, we observe fractional Shapiro steps and Fraunhofer patterns, consistent with the existence of two degenerate Josephson ground states related by time-reversal symmetry (TRS). By programming the JJ current bias sequence, we controllably break TRS to place the JJ into either of the two ground states, realizing reversible Josephson diodes without external magnetic fields. Our results open a path to engineering topological devices at higher temperatures.