Reverse circulation hydraulic fishing and grabbing fishing socket and fishing method

The invention provides a reverse circulation hydraulic salvaging cylinder and salvaging method.The salvaging cylinder comprises an upper connector, an outer cylinder, a salvaging outer sleeve and a milling shoe which are sequentially connected from top to bottom, a cylindrical structure with an axial center channel is formed by the components, and a piston, an inner cylinder and a salvaging claw which are sequentially connected from top to bottom are arranged in the axial center channel; wherein the piston is arranged in the upper connector through the shear pin, an inclined hole with a nozzle is formed in the pipe wall of the upper connector and the piston, non-free jet flow is formed at the well bottom, the vacuum degree at the nozzle is increased, local reverse circulation is achieved, the jet flow passes through an annular space and a milling shoe, carries scrap iron and returns into the fishing barrel, and the scrap iron is filtered through the grabbing teeth or the slip insert and the filter pipe. And t