In this paper, the Glauber dynamics for the Ising model on the complete multipartite graph $K_{np_1,\dots,np_m}$ is investigated where $0<p_i<1$ is the proportion of the vertices in the $i$th component. We show that the dynamics exhibits the cutoff phenomena at $t_n = \frac{1}{2(1-β/β_{cr})} n\ln n $ with window size $O(n)$ in the high temperature regime $β< β_{cr}$ where $β_{cr}$ is a constant only depending on $p_1,\dots,p_m$. Exponentially slow mixing is shown in the low temperature regime $β>β_{cr}$.