Alumina (Al2O3) is an extremely hard and brittle ceramic that is usually used as an abrasive or a cutting tool insert in manufacturing. However, its growing applications in industrial products make it necessary to conduct a study of the machinability of alumina themselves with a cost-effective and flexible method, rather than conventional diamond grinding or laser-assisted processing methods. In this paper, polycrystalline diamond tools are used to investigate the machining of nonporous pure alumina by applying an inclined ultrasonic elliptical vibration cutting (IUEVC) method. First, a theoretical analysis is presented to study the effects of the machining parameters on cutting performances during raster cutting procedures from the prospective of the material removal rate (MRR), tool-chip contact area, cutting edge angle, etc. Then, experiments are carried out to investigate the cutting forces and the areal surface roughness (Sa) in connection with the theoretically established relationships. The results show that the cutting forces are remarkably reduced, by up to more than 90%, and that the machined surface finish is also improved compared with conventional methods.