<p>The Gauge-Uzawa method is a fully discretized projection-type method that has been widely applied to the numerical solution of fluid dynamics problems. Inspired by this method, two first-order Gauge-Uzawa finite element methods are proposed for the unsteady magneto-micropolar equations (MMEs). In both cases, temporal discretization is based on the first-order backward differentiation formula, with linear terms treated implicitly and nonlinear terms handled semi-implicitly, while the linear velocity, angular velocity, and magnetic field are coupled in one case and fully decoupled in the other. Unconditional stability for both methods is rigorously established via energy estimates. Numerical experiments are conducted to validate the theoretical accuracy and illustrate the efficiency and robustness of the proposed methods.</p>