This paper presents a cutting plane algorithm for multiclass maximum margin clustering (MMC). The proposed algorithm constructs a nested sequence of successively tighter relaxations of the original MMC problem, and each optimization problem in this sequence could be efficiently solved using the constrained concave-convex procedure (CCCP). Experimental evaluations on several real world datasets show that our algorithm converges much faster than existing MMC methods with guaranteed accuracy, and can thus handle much larger datasets efficiently.