How to draw the graph of f(x,y) = x * y ?

The function curve() draws the graph of functions from R to R. Is
there some homologous function to curve() to draw functions from R^2
to R?

No, you would have to write it yourself.  The basic idea is to use outer()
to construct a matrix of function evaluations, then plot the matrix using
persp, contour, image, rgl::persp3d, etc.  There are examples on the
?contour man page.