The invention provides a clamping device for feeding and discharging. The clamping device comprises a mounting base and a clamping jaw mechanism used for clamping workpieces, wherein the clamping jaw mechanism comprises a plurality of clamping heads; each clamping head is movably connected with the mounting base, and is provided with a working surface and a plurality of floating mechanisms; the floating mechanisms are positioned on the working surface, and each of the floating mechanisms comprises a floating piece; each floating piece is in floating connection with the corresponding clamping head. The floating pieces are arranged on the working surface of each of the clamping heads, so that during clamping the workpieces by the clamping jaw mechanism, when the workpieces are clamped by the clamping heads, the floating pieces act on the surface of each of the workpieces to realize the function of clamping; besides, each of the floating pieces is in floating connection with the corresponding clamping head, so that after being clamped, the workpieces have certain space for free moving, and the workpieces are prevented from being ''completely clamped''. Through the adoption of the clamping device disclosed by the invention, the workpieces can be flexibly mounted at right positions, and rigid damages on the surfaces of the workpieces are avoided. In addition, the invention further provides a robot with the clamping device for feeding and discharging.