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For context, my character just got pounded by flaming boulders. She is currently immune to fire for story reasons, so the fire damage is null. However, she has to make a dexterity saving throw against the bludgeoning damage. It deals 60 damage, however if she succeeds she takes half damage.

What happens if she rolls a natural 20?

I know the damage is halved because she did succeed, but are there any other reductions to damage because of her natural 20 roll?

(Note: For our house rules we play with the premise that a natural 20 is an automatic success and a natural 1 is an automatic fail)

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No

Rules as written (and excluding house rules or specific rules for the effect that called for a save) there is no added effect from rolling a 20 on a saving throw (nor ability check).

The general description of saving throws in the Player's Handbook (p. 179) make no mention of rolling a 20 (nor a 1). However, the DMG section on ability checks and saving throws includes a subsection on Critical Success or Failure (p. 242) which says a DM can choose to have extraordinary outcomes on a roll of 1 or 20, but it opens with:

Rolling a 20 or a 1 on an ability check or a saving throw doesn't normally have any special effect.

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  • \$\begingroup\$ It still confuses me, coming off of 3.5e, that outside of an attack roll a 20 is just another number. Maybe someday I'll fully make the adjustment. \$\endgroup\$ – Upper_Case Dec 10 '19 at 16:56
  • \$\begingroup\$ @Upper_Case-StopHarmingMonica Isn't 20 just another number outside of attack rolls in 3.5e? \$\endgroup\$ – Andy M Dec 10 '19 at 17:55
  • \$\begingroup\$ @AndyM It's been a while, but as I recall natural 20s and 1s were automatic successes and failures, respectively, for skill checks as well in 3.5. My books are at home so I can't check right now, but if I'm mistaken then I'm even more mixed up on that (house) rule than I'd thought! \$\endgroup\$ – Upper_Case Dec 10 '19 at 17:56
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    \$\begingroup\$ @Upper_Case-StopHarmingMonica In 3.5, natural 20s and 1s are automatic successes and failures for a) attack rolls and b) saving throws. Nothing else. For skill checks, they're just numbers. \$\endgroup\$ – Douglas Dec 10 '19 at 19:31
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No, you do not negate extra damage.

When making a saving throw, there is no such thing as a critical success nor critical failure. When you roll a 1 or a 20, simply add any relevant modifiers to that saving throw and use that total. The only exception to this is with a death saving throw (see basic rules, p. 76):

Whenever you start your turn with 0 hit points, you must make a special saving throw, called a death saving [...] Unlike other saving throws, this one isn’t tied to any ability score. [...]

Rolling 1 or 20. When you make a death saving throw and roll a 1 on the d20, it counts as two failures. If you roll a 20 on the d20, you regain 1 hit point.

So, in your example, the character rolling a 1 on the Dexterity saving throw will take the full damage, unless she meets the DC with her Dexterity saving throw modifier. If she rolls a natural 20, she can still fail the saving throw if the DC is higher than the roll plus her bonuses.

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