The oscillation of neutral dynamic equations on time scales has important implications in both theory and application. This paper considers the oscillation of a class of second-order neutral dynamic equations with mixed nonlinearities. Firstly, the neutral coefficient function $\pi(t)$ is defined. By means of the generalized Riccati transformation technique and the averaging technique, we establish some new oscillation criteria for the second-order neutral dynamic equations under the case $\pi(t_{0})=\infty$. Then, when $\pi(t_{0})<\infty$, by strengthening the assumptions and using some inequalities and some analytic techniques, we also obtain several oscillation criteria for the equations. Our work generalizes and improves some known results in the literature for oscillation of second-order neutral dynamic equations. Finally, two examples are presented to illustrate the importance of our results.