Removing terms of certain degree in multivariable polynomial

poly = a x^2*y - b x*y - c x*y^2 + d x + e y;
var = {x, y};

FromCoefficientRules[Select[CoefficientRules[poly, var], Total@#[[1]] == 3 &], var]

a x^2 y - c x y^2

Tr[Select[MonomialList[poly],Tr[Exponent[#,{x,y}]]==3&]]

a x^2 y-c x y^2

Another route:

d = 3;
poly = a x^2*y - b x*y - c x*y^2 + d x + e y;
var = {x, y};

Fold[Dot, CoefficientArrays[poly, var][[d + 1]], ConstantArray[var, d]]
   x (a x y - c y^2)