Magnonics promises low-dissipation information processing, yet spin-polarized magnon transport requires magnetic fields or spin–orbit couplings. Altermagnets exhibit spin-polarized electronic states and zero net magnetization. However, achieving large magnon spin splitting and robust magnonic spin currents remains challenging. Here we show that twisted van der Waals antiferromagnets provide a symmetry-tunable platform for the altermagnetic magnons. Alternating intralayer exchange arises in twisted bilayers lacking inversion and horizontal mirror symmetries, rendering nonrelativistic magnon spin splitting. Breaking out-of-plane rotational symmetries of a constituent monolayer significantly enhances low-energy splittings. We illustrate general conclusions in twisted CrPS₄ (d-wave) and CrI₃ (i-wave) bilayers. Moreover, pronounced field-free spin currents, characterized by robust spin Seebeck and spin Nernst effects, emerge in CrPS₄. Remarkably, the spin transport is efficiently tuned by twist angle and exceeds that of conventional altermagnets by orders of magnitude. Our work provides novel insights into controlling magnons, deepening our fundamental understanding of altermagnetic spintronics.