Cytoplasmic flows, bacterial colonies, and algal blooms are ubiquitous examples of active suspensions assembled from self-propelled particles, which internally inject energy into their suspending medium and, at sufficient concentrations, can produce large-scale flows. Linking macroscale material properties of active suspension to their underlying microscopic dynamics is a key challenge to describing these materials. Relying on the unique properties of microtubule based active matter and state of the art rheological techniques we measured the shear-rate-dependent viscosity, yield stress, and local dynamics of a model active suspension, while simultaneously quantifying their microscopy dynamics and autonomous flows. Our microtubule suspensions form a transient network with long-range mechanical contacts mediated by motor proteins and are best described as active gels. We find that activity coupled with external shear dramatically alters their apparent viscosity. We develop a simple model to explain the fundamental connection between an external deformation and microscopic dynamics that produce an anomalous mechanical response in active gels.