  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-\beta/\beta_{cr})} n\ln n
$ with window size $O(n)$ in the high temperature regime $\beta< \beta_{cr}$
where $\beta_{cr}$ is a constant only depending on $p_1,\dots,p_m$.
Exponentially slow mixing is shown in the low temperature regime
$\beta>\beta_{cr}$.
