The invention provides a surgical instrument of a surgical robot and the surgical robot, wherein the surgical instrument of the surgical robot comprises a first bracket, a transmission assembly, a surgical executing part, a second bracket and a driving assembly, wherein the transmission assembly is arranged on the first bracket and comprises a magnetic transmission piece; the surgical executing part is connected to the transmission assembly; the second bracket is detachably connected to the first bracket; the driving assembly is arranged on the second bracket and comprises a magnetic driving piece which is adaptive to the magnetic transmission piece, wherein the magnetic transmission piece and the magnetic driving piece are connected through magnetic force when the first bracket and the second bracket are connected; and the driving assembly enables the surgical executing part to move by driving a driven assembly to move. According to the surgical instrument of the surgical robot provided by the invention, motion control over the surgical executing part is realized, so that the surgical executing part can adjust own position or angle in accordance with actual demands; therefore, flexibility of the device (the surgical instrument) is enhanced, and an operation or treatment is further facilitated.