L want to completely remove the tailgate of a 1998 Chevrolet S10 pickup.

You'll have to open the tailgate first
If the latch handle on the tailgate is broken or the release bar and clips disconnected from the latch handle then;
Lift up on the latch release with one hand and move the release cable manually to disengage the spring loaded latch plates that are bolted into the truck body- this should allow the striker pins (that are secured to the tailgate itself), to be freed.
If the tailgate itself is somehow binding to the truck body when you use the latch release, you may have to use a screwdriver or pry bar to force the tail down; or in an extreme case, use a second person to kick the tailgate while you activate the release latch or cable.
Once the tailgate folds down, it's just a matter of releasing the support brackets from the hinges as well as the wire cable.
Hope this helps.

Really bad idea. This will cost you lower fuel mileage, danger of cargo loss. Mythbusters have run tests proving that the aero effects with the tailgate up form a cushion of air in the bed which reduces drag. None of my business I know.