To simplify and then evaluate the given expression $(3x^{2}y-xy^{2})-2(-2xy^{2}+x^{2}y)$ with $x=2$ and $y=-1$, we follow these steps:

1. Simplify the expression:

First, distribute the negative sign inside the parentheses:
$$\begin{align*} (3x^{2}y-xy^{2})-2(-2xy^{2}+x^{2}y) &= 3x^{2}y-xy^{2}+4xy^{2}-2x^{2}y \\ &= x^{2}y + 3xy^{2}. \end{align*}$$

2. **Substitute $x=2$ and $y=-1$:**

Next, substitute $x=2$ and $y=-1$ into the simplified expression:
$$\begin{align*} x^{2}y + 3xy^{2} &= (2)^{2}(-1) + 3(2)(-1)^{2} \\ &= 4(-1) + 3(2)(1) \\ &= -4 + 6 \\ &= 2. \end{align*}$$

Therefore, after simplifying the original expression and substituting the given values of $x$ and $y$, we find that the value of the expression is $\boxed{2}$.