Not sure what you are asking - energy exerts a gravitational field, whether the energy is in its rest form (i.e. mass) or its kinetic form (what we normally think of as energy). Gravitational fields produce a gravitational potential well, in which something falling into that well picks up kinetic energy (losing rest energy) as it does so. So, for example, the space shuttle is ever so slightly more massive when it is in orbit than when it is on the ground, because when it is on the ground it is deeper into the Earth's potential well. The only way to release the "stored"energy is to fall into the well.

As an example, you may be familiar with a medieval siege engine called a trebuchet (TRAY-beu-SHAY), which operates by having a large weight on the end of a lever arm, and letting the weight fall swings the lever that in turn hurls a projectile. The weight falling into the Earth's potential well releases its energy that is then transferred via the lever arm into the missile, which is usually a boulder. If you saw the cinematic adaptation of The Return of the King(the third volume of the Lord of the Rings trilogy),the soldiers on the walls of Minas Tirith were using war machines to hurl blocks of masonry at Sauron's armies - those were trebuchets.

It's not possible to suck the energy out of the Earth's gravitational field such that the Earth has no gravity, however.