In this paper, we studied the geometry of sweeping surfaces generated by the involutes of spacelike curves with a timelike binormal in Minkowski 3-space $E_1^3$. First, we investigated the singularity concept, and the mean and Gaussian curvatures of these surfaces. Then, we provided the requirements for the surface to be developable (flat) and minimal. We also determined the sufficient and necessary conditions for the parameter curves of these surfaces to be geodesic and asymptotic. Moreover, we analyzed these surfaces when the parameter curves are lines of curvature on the surface. Finally, the examples of these surfaces were given and their corresponding figures were drawn.