Precise control at the colloidal scale is one of the most promising bottom-up approaches to fabricating new materials and devices with tunable and precisely engineered properties. Magnetically driven colloidal assembly offers great versatility because of the ability to externally tune particle-particle interactions and to construct a host of particle arrangements. However, despite previous efforts to probe the parameter space, global orientational control in conjunction with two-dimensional microstructural control has remained out of reach. Furthermore, the magnetic relaxation time of superparamagnetic beads has been largely overlooked despite being a key feature of the magnetic response. Here, we take advantage of the magnetic relaxation time of superparamagnetic beads in an alternating rotating magnetic field and show how harnessing this feature facilitates the formation of oriented clusters. The orientation of these clusters can be controlled by field parameters. Using experiments, simulations, and theory, we probe a two-particle system (dimer) under this alternating rotating magnetic field and use its dynamics to provide insights into the collective response that forms clusters. We find that the type of field has significant implications for the dipolar interactions between the colloids because of the nonnegligible magnetic relaxation. Moreover, we find that the competing time scales of the magnetic relaxation and the alternating field generate an anisotropic interaction potential that drives cluster alignment. By exploiting the magnetic relaxation time of magnetic systems, we can tailor new types of interparticle interactions, thereby expanding the capabilities of colloidal assembly in engineering unique materials and devices.