Mechanically operated reverse cementing crossover tool

A crossover tool for use in a wellbore includes: a tubular housing having a bypass port; a mandrel having a bore therethrough and a mandrel port in fluid communication with the mandrel bore, the mandrel movable relative to the tubular housing between a first position where the mandrel port is isolated from the bypass port and a second position where the mandrel port is aligned with the bypass port; and an actuator operable to move the mandrel between the first position and the second position. The actuator includes a first piston connected to the mandrel and a second piston operable in response to the first piston.