I am having trouble trying to remove the spare tire from under the envoy. It seems to be just hanging there and can spin but will not come off. I do not know how to remove the bracket that is holding it on. Please help

Since the spare is mounted under the rear of the car, Its not easy...you have to assemble the long crank rod out of its two pieces, then feed the rod through the hole in the top of the rear bumper and lock it into the mechanism that holds the tire in place. Once the crank rod is locked in, lower the tire towards the ground. Once the tire is low enough, you can crawl under the car and release the tire from its mount. The hardest part is locking the crank rod into the spare tire mechanism through the hole in the bumper.

You will have to get from dealers parts counter

Rotate the hoist shaft counterclockwise in order to lower the spare tire to the ground. Continue to rotate the shaft until the spare tire can be pulled out from under the vehicle and removed. If the spare tire does not lower to the ground, the secondary latch is engaged causing the tire not to lower.

If the secondary latch is engaged and the cable end is visible, perform the following procedure: 3.1. Tighten the cable by rotating the hoist shaft clockwise until you hear 2 clicks or feel it skip twice. You cannot overtighten the cable. 3.2. Loosen the cable by rotating the hoist shaft counterclockwise 3 or 4 turns. 3.3. If the spare tire can be lowered, repeat steps 1 and 2 to see if the spare tire can be removed. 3.4. If the spare tire cannot be lowered, rotate the hoist shaft counterclockwise until approximately 15 cm (6 in) of cable is exposed. 3.5. Raise and support the vehicle. 3.6. Place a transmission jack, or equivalent, under the spare tire. 3.7. Position the center of the transmission jack under the secondary latch release button at the center of the spare tire. Arrange the arms of the transmission jack so they will support the tire after it has been released. 3.8. Raise the jack until the spare tire stops moving upward and is firmly held in place, releasing the secondary latch. 3.9. Lower the tire. If the spare tire is hanging by the cable, rotate the hoist shaft counterclockwise until the tire is low enough to remove.

If the spare tire does not lower to the ground,the secondary latch is engaged
causing the tire not to lower Your vehicle has an underbody-mounted tire hoist
assembly equipped with a secondary latch system.It is designed to stop the spare
tire from suddenly falling off your vehicle if the cable holding the spare tire
is damaged.For the secondary latch to work,the tire must be stored with the
valve stem pointing up.
1.Check under the vehicle to see if the cable is visible.If it is not visible
proceed to Step 6.
2.If visible,first try to tighten the cable by turning the wheel wrench clockwise
until you hear two clicks or feel it skip twice.You cannot overtighten the cable.
3.Loosen the cable by turning the wheel wrench counterclockwise three or four turns.
4.Repeat this procedure at least two times.If the spare tire lowers to the ground
continue with Step 2 of removing the Spare.
5.Turn the wrench counterclockwise until approximately 6 inches (15 cm) of cable is
exposed.
6.Attach the jack handle,extension and the wheel wrench to the jack and place it under
the vehicle towards the front of the rear bumper.Position the center lift point of the
jack under the center of the spare tire.
7.Turn the wrench clockwise to raise the jack until it lifts the end fitting.
8.Continue raising the jack until the spare tire stops moving upward and is held firmly
in place.
9.Lower the jack by turning the wheel wrench counterclockwise.Keep lowering the jack
until the spare tire slides off the jack or is hanging by the cable.
10.Disconnect the jack handle from the jack and carefully remove the jack.Use one hand
to push against the spare while firmly pulling the jack out from under the spare tire
with the other hand.

The short answer is look in your owner's manual. If you don't have one, go to www.trailvoy.com and check in the resources section. There should be a link there for 2004 Envoy owner's manual.
Be aware that the spare tire winch mechanism should be exercised once in a while to keep it working freely.

The tools are under the second row seats. The hole for the spare tire lowering mech. is above the rear bumper when you lift the tail gate. Put the proper tool down the hole, turn counter clockwise, lowers spare. Reverse to bring up.

I had the same problem and the shop I took it to couldn't get it off either. But I opted for them not to cut it off and I took the truck home to diagnose what the problem was. So to make this short, I got the spare down and the only way you can do the same is by using a flat head screw driver, pliers, and some "Deep Creep" penetrating oil. 
First: if you have the tire down the standard 2" or so, take your pliers and pull at the base of the cable "downwards". (the cable should free from the bracket under the tire that holds it up).
-Then spray penetrating oil around the bracket as this is what is causing it not to release. In the manual it suggests pushing it back up with the jack until it clicks to allow it to come down. Most likely this will not work as dirt and corrosion will freeze the mechanism that acts as the secondary lock. 
-Take your jack and lift up your spare, holding the weight on the rim and not the bracket attached to the winch. This should free up the winch to allow movement. Then taking your flat head screw driver and you will likely need a flash light, look up into the hole where the cable comes from. You will see there are two little teeth attached to it inside holding it to the frame of the winch. First try prying the teeth away from the lip of the hole to allow the bracket to drop. If this doesn't work, then stick your flat head in between the sides of the arm attached to the teeth and pry outwards, allowing the arm to free up enough to allow movement.
This should drop your tire down and avoid the expense of buying another winch after cutting yours. 
Good luck!

the instructions and tools should be under the second row seats.

Well catch 22 here, you have to remove the tire to get at the cable reel, have it cut off with a high speed cut off wheel.

I found the secret, The tire is suspended buy a cable on a winch, there is a nut on the right hand side under the carpet when you open the rear hath. You turn that counter clockwise to lower and you turn the support sideways trough the hole in rime of tire.