Landauer's erasure principle puts a fundamental constraint on the amount of work required to erase information using thermal reservoirs. Recently this bound was improved to include corrections for finite-sized thermal reservoirs. In conventional information-erasure schemes, conservation of energy plays a key role with the cost of erasure. However, it has been shown that erasure can be achieved through the manipulation of spin angular momentum rather than energy, using a reservoir composed of energy-degenerate spin particles under the constraint of the conservation of spin angular momentum, in the limit of an infinite number of particles. In this case the erasure cost is in terms of dissipation of spin angular momentum. Here we analyze the erasure of memory using a finite-sized spin reservoir. We compute the erasure cost to compare it with its infinite counterpart and determine what size of finite reservoir gives similar erasure cost statistics using the Jensen-Shannon Divergence as the measure of difference. Our findings show that erasure with finite-sized reservoirs results in the erasure of less information compared to the infinite reservoir counterpart when compared on this basis. In addition we discuss the cost of resetting the state of the ancillary spin particles used in the erasure process, and we investigate the degradation in erasure performance when a finite reservoir is repeatedly reused to erase a sequence of memories.