This work presents a soft manipulator for minimally invasive surgery inspired by the biological capabilities of the octopus arm. The multi-module arm is composed of three identical units, which are able to move thanks to embedded fluidic actuators that allow omnidirectional bending and elongation, typical movements of the octopus. The use of soft materials makes the arm safe, adaptable and compliant with tissues. In addition, a granular jamming-based stiffening mechanism is integrated in each module with the aim of tuning the stiffness of the manipulator and controlling the interactions with biological structures. A miniaturized camera and a pneumatic gripper have been purposely designed and integrated on the tip of the manipulator making it usable in real working conditions. This work reports the design and the fabrication process of the manipulator, the theoretical and experimental evaluation of the stiffness and the analysis of the motion workspace. Finally, pick and place tests with the fully integrated system are shown.