On a successful save when the spell is cast you are staggered for 1 round.
On a failed initial save, on the targets next turn they fall unconscious and are at 0 hp. On their 2nd turn after failing the initial save they can make another save, if they fail again they drop to -1 hp and are dying. If they succeed they continue to be at 0 hp and unconscious, but still make the save on the 3rd turn because the spell works for 3 rounds. On the 3rd round after the initial save they must make a save. If they succeed they would stay at their previous condition (either at 0 hp and unconscious if they failed only the initial save, or at -1 hp and dying if they failed both the initial and 2nd save). If they fail they progress one step further along the track. Either to dead if the target failed all 3 saves, or to -1 hp and dying if they failed only 2 of the 3 saves.
Is there any defense against suffocation or it's big brother Mass Suffocation? Aside from not requiring breathing in the first place,
antimagic shell or spellbane.
Greater Spell Immunity for Suffocation, Spell Turning for both.
An ion stone with wayfinder and the Nightgaunt Mask are the only items I know that remove the need to breathe. Iron Body and incorporeal spell effects will also make you immune. You can also dispel it if you fail the first save and are a psychic caster or have a buddy do it for you.
There are class features that remove the need to breathe, I believe.
Fort saves are always a good defense.
Chaokineticist can get no breath. Not sure of any others, probably an Oracle mystey.
Your GM is ruling incorrectly.
Suffocation is a great emergency spell, but as with all save-or-die* spells, only break it out in emergencies. The GM and your party members will get bored and/or aggravated if you either win the fight by yourself or contribute nothing due to a successful save.
My dm is ruling it that they get an additional save in the same round i cast the spell on their turn making the spell barely worth taking....
Your GM is incorrect. But the spell is very powerful when it works (knocking an enemy unconscious from a single failed save), so it's not an uncommon reaction to nerf these types of spells.
Talk to your GM about how the spell works and explain what you learned here, and then ask him if he would simply prefer if you didn't use these types of spells. If he's going to nerf the spell anyways, you may as well just not use and at least if you offer voluntarily not to use it he might rule more favorably on things for you in the future.
Thank you Plausible Pseudonym, those are good finds! Spell Turning on a BBEG is nasty surprise for a SoD happy PC.