We were playing a commander game and the attacking player had a bunch of trample creatures, well call him Andy. The defending player, Bob, blocks with a Zulaport Cutthroat, Cruel Celebrant, Teysa Karlov, and at least 2 other creatures. Normally that would be enough to save him as he was at 37 life but then Andy played Savage Beating choosing to give his army double strike. Andy was at 3 life. So the question is does he die before the regular damage gets to kill Bob or is it too late and they're both dead?
You have left several crucial details out of your description of the situation, which makes it a bit difficult to analyze.
Under the assumptions that:
- Andy was attacking with more than 5 creatures.
- Andy's creatures that were not blocked, could do a total of 37 damage after the second phase (but less than 37 damage during the first strike phase).
- Andy's creatures killed at least one of Bob's creatures.
- No other shenanigans in play (trample, damage prevention, regeneration, no other first strike etc.).
- First strike damage is assigned.
- One or more of Bob's creatures die.
- Triggers from Bob's creature deaths, due to Zulaport et al. go on the stack in Bob's chosen order.
- After the resolution of each trigger, state-based actions are checked. One of those is whether or not Andy has more than 0 life.
- When a trigger resolves that puts Andy at zero life, he is dead. He leaves the game, along with all permanents that he owns.
- All remaining triggers on the stack that target Andy fizzle, and Bob lives.
For lots of info on exactly how all the edge cases of player death are handled, see this question:
For when players actually die, see this question for a full explanation:
- Combat Phase
506.1. The combat phase has five steps, which proceed in order: beginning of combat, declare attackers, declare blockers, combat damage, and end of combat. The declare blockers and combat damage steps are skipped if no creatures are declared as attackers or put onto the battlefield attacking (see rule 508.8). There are two combat damage steps if any attacking or blocking creature has first strike (see rule 702.7) or double strike (see rule 702.4).
- Combat Damage Step
510.1. First, the active player announces how each attacking creature assigns its combat damage, then the defending player announces how each blocking creature assigns its combat damage. This turn-based action doesn’t use the stack. A player assigns a creature’s combat damage according to the following rules:
510.1a Each attacking creature and each blocking creature assigns combat damage equal to its power. Creatures that would assign 0 or less damage this way don’t assign combat damage at all.
After the mandatory actions in the first combat damage step, state-based actions are checked and they'll see an Andy with 0 or less life, and he'll lose the game. Then,
104.5. If a player loses the game, that player leaves the game. If the game is a draw for a player, that player leaves the game. The multiplayer rules handle what happens when a player leaves the game; see rule 800.4.
800.4a When a player leaves the game, all objects (see rule 109) owned by that player leave the game and any effects which give that player control of any objects or players end.
So Andy's creatures aren't around in the second combat damage phase, and Bob will survive.