Conventional fluid-driven soft grippers typically depend on external sources, which limit portability and long-term autonomy. This work introduces a self-contained soft gripper with fixed size that operates solely through internal liquid redistribution among three interconnected bistable snap-through chambers. When the top sensing chamber deforms upon contact, the displaced liquid triggers snap-through expansion of the grasping chambers, enabling stable and size-selective grasping without continuous energy input. The internal hydraulic feedback further allows passive adaptation of gripping pressure to object stiffness. This source-free and compact design opens new possibilities for lightweight, stiffness-adaptive fluid-driven manipulation in soft robotics, providing a feasible approach for targeted size-specific sampling and operation in underwater and field environments.