The geometries, stabilities, electronic, and magnetic properties of $Au_{n}Sc_{m}$ $(n=1-7,$ $m=1,2)$ clusters have been systematically investigated by density functional theory. It is shown that the most stable structures of $Au_{n}Sc (n=1-7)$ clusters favor planar structure and $Sc$ atom is prone to occupy the center site of $Au$ atoms ring. For $Au_{n}Sc_{2}$ clusters, the 3d configurations become the lowest energy structure for $n\geq3;$ the growth is based on triangle bipyramid structure of $Au_{3}Sc_{2}$ cluster except $Au_{4}Sc_{2}.$ The second-order energy difference and the fragmentation energy show $Au_{3}Sc,$ $Au_{5}Sc,$ $Au_{3}Sc_{2}$ and $Au_{6}Sc_{2}$ clusters possess relatively higher stabilities than their neighbor size. The doping of $Sc$ atom can greatly improve the stability of $Au$ clusters. The doped one $Sc$ atom changes the odd-even alternation trend of gaps in $Au_{n}.$ The two doped-Sc atoms enhance chemical activity of $Au_{n}$ in most cases. The total magnetic moments with even valence electrons are quenched on the whole due to electron pairing effects. The averaged coordination number for Sc should be major reason for reduce of local magnetic moments of $Sc$ atom with cluster size increasing in cluster with odd valance electrons. The total magnetic moments in $AuSc$ and $Au_{2}Sc_{2}$ are no quenched due to the smaller coordination number, the charge transfer and weak hybridization between the $Sc$ and $Au$ atoms.