We formulate axion magnetohydrodynamics beyond the ideal limit, retaining axion inertia and the essential physics of non–ideal plasmas from first principles. In this framework, regions where magnetic flux freezing breaks down acquire a new physical role: whenever $𝐄\cdot 𝐁\ne 0$, magnetic dissipation acts as a localized source of axion radiation. We show that magnetic reconnection naturally excites mixed Alfv'en–axion modes, enabling coherent energy exchange between magnetic fields and axions in magnetically dominated environments. In neutron stars and magnetars, this mechanism leads generically to transient axion bursts powered by reconnection–driven Alfv'enic dissipation. We connect this production process to observational prospects and derive a characteristic sensitivity to the axion–photon coupling, complementary to searches based on static magnetic fields.