To simplify the given expression $-2(a^{3}-3b^{2})+4(-b^{2}+a^{3})$, we distribute the coefficients and combine like terms as follows:

$$\begin{align*} -2(a^{3}-3b^{2})+4(-b^{2}+a^{3}) &= -2a^{3} + 6b^{2} + 4a^{3} - 4b^{2} \\ &= (-2a^{3} + 4a^{3}) + (6b^{2} - 4b^{2}) \\ &= 2a^{3} + 2b^{2}. \end{align*}$$

Therefore, the simplified form of the given expression is $\boxed{2a^{3} + 2b^{2}}$.