dnd 5e: if you throw a save shot where you only receive half the damage in a success, do you reduce the damage even more in a Natural 20?

When making a saving shot, there is no critical success or critical failure. When you take a 1 or a 20, simply add the relevant modifiers to that save throw and use that total. The only exception to this is with a throw of salvation (see basic rules, p. 76):

Whenever you start your turn with 0 hit points, you must make a special save shot, called death save (…) Unlike other save shots, this is not linked to any skill score. (…)

Rolling 1 or 20. When you make a death saver shot and roll a 1 in d20, it counts as two failures. If you get a 20 in d20, you recover 1 hit point.

Then, in your example, the character who rolls a 1 on the Dexterity save throw will take full damage, unless he meets the DC with his Dexterity save throw modifier. If you take a natural 20, the save throw may still fail if the DC is higher than the throw plus your bonuses.