A medical system for treating an internal tissue opening can include a closure device and associated delivery device. The closure device can include a multi-cellular body portion operatively associated with a first anchor and a second anchor. The closure device can be configured to apply lateral force to tissue of the internal tissue opening for tissue approximation. The closure device can have a substantially flat aspect, and have a depth that is substantially greater than the thickness of a majority of the members forming the closure device. The closure device can also include an in-growth material. The delivery device can include an actuating assembly configured to partially deploy the closure device by a first movement, and deploy a second portion of the closure device by a second movement. The delivery device can also include a release assembly to selectively release or disconnect the closure device from the delivery device.