A tissue gripping device is formed from a shape-memory material, and has a base section, a first arm, and a second arm disposed opposite the first arm, each arm having a first end coupled to the base section and a free end extending from the base section. The arms of the tissue gripping device are configured to resiliently flex toward a relaxed configuration in a distal direction as the tissue gripping device is moved from a pre-deployed configuration toward a deployed configuration. The tissue gripping device is usable in a method for gripping tissue. The method includes positioning the tissue gripping device near target tissue and moving the tissue gripping device from a pre-deployed configuration toward a deployed configuration in order to grip the target tissue.