We demonstrate that superconducting unconventional magnet junctions harbor transverse spin and charge diode effects with perfect rectification efficiencies. This nonreciprocal transverse transport is governed by the interplay of mirror reflections and spin rotation with respect to the Néel vector, a mechanism that is universally applicable to all unconventional magnets. Interestingly, the transverse spin diode features pure spin currents, while the charge diode yields spin-polarized charge currents, both exhibiting highly controllable rectification functionalities at vanishing net magnetization. Our results position superconducting unconventional magnets at the forefront of orthogonal engineering in next-generation transverse superconducting spintronics.