Functions of several variables composition

If we have two functions $G,F:mathbb R^2tomathbb R^2$ then the mechanism
$Fcirc G(x,y)=F(G(x,y))$ gives us a new map $Fcirc G:mathbb R^2tomathbb R^2$ called its composition.

In a "schematic" view, and with two functions for an example,
we would write
$$
left(begin{array}{c}x\yend{array}right)
stackrel{G}to
left(begin{array}{c}x^2y\2yend{array}right)qquad {rm and}qquad
left(begin{array}{c}x\yend{array}right)
stackrel{F}to
left(begin{array}{c}x-y\xend{array}right)
$$
then
$$
left(begin{array}{c}x\yend{array}right)
stackrel{Fcirc G}longrightarrow
left(begin{array}{c}x^2y-2y\x^2yend{array}right).
$$

How could this process be programmed in Mathematica12?