Loose abrasive grinding and bound abrasive grinding are two principal grinding methods in optical cold process, but they are different in grinding removal mechanism. Nd-doped phosphate glasses are dominating materials in high average power laser solid state lasers. For little investigative experience in subsurface damage (SSD) in Nd-doped phosphate glasses, this paper investigated the grinding removal mechanism using different bound diamond abrasives. The effects of abrasive size, load, spindle speed, bonding material and the coolant on the subsurface damage in Nd-doped phosphate glasses were surveyed as well. Subsurface damage produced by loose abrasives was presented for comparation. All the results provide essential foundation for choosing and optimizing fabrication technology of high-quality Nd-doped phosphate glasses.