The result is correct and is exactly what was requested in the input. If a result based on total degree is wanted, best is to a univariate substitution, as done here. In brief:
f[x_, y_] = Sin[1 + x + y]/(2 + Cos[2 - x + y]);
seri1 = N[Expand[Normal[
Series[f[x, y] /. Thread[{x, y} -> t*{x, y}], {t, 0, 1}]] /. t -> 1]]
(* Out[276]= 0.531280931986 + 0.0361207230645 x + 0.646142403765 y *)
