The aim of this paper is to give oscillation criteria for the third-order quasilinear neutral delay dynamic equation \[ \Big[r(t)\Big(\big[x(t)+p(t)x(\tau_0(t))\big]^{\Delta\Delta}\Big)^y\Big]^\Delta+q_1(t)x^\alpha(\tau_1(t))+q_2(t)x^\beta(\tau_2(t))=0, \] on a time scale $\Bbb T$, where $0<\alpha<\gamma<\beta$. By using a generalized Riccati transformation and integral averaging technique, we establish some new sufficient conditions which ensure that every solution of this equation oscillates or converges to zero.