In the present article, we construct a new sequence of bivariate Szász-Durrmeyer operators based on Dunkl analogue. We investigate the order of approximation with the aid of modulus of continuity in terms of well known Peetre's K-functional, weighted approximation results, Voronovskaja type theorems and Lipschitz maximal functions. Further, we also discuss here the approximation properties of the operators in Bögel-space by use of mixed-modulus of continuity