The invention discloses a cylinder-driving swing support device and an oil press. The swing support device comprises a stand column, a cylinder fixing support base mounted on the stand column and used for supporting a cylinder, and an integral mounting base mounted on the stand column; a support arm mounting base is mounted on the integral mounting base, and a swing support arm capable of swing in a reciprocating manner around the support arm mounting base under the driving of the cylinder is hinged to the support arm mounting base; one end, hinged to the support arm mounting base, of the swing support arm serves as a hinge end, and the other end of the swing support arm serves as a swing end; and the swing end of the swing support arm is provided with a bending section, and a locking hole for allowing the bending section of the swing support arm to stretch in when the piston rod of the cylinder stretches out completely is formed in the stand column. The cylinder-driving swing support device provided by the invention has a small and exquisite structure, is flexible in motion, has large supporting force, and is convenient to achieve an automatic control function.