The rules are unclear
It was confirmed that trolls could suffocate in Pathfinder, as shown in this answer. But the rules actually say the opposite (as shown in this answer), the regeneration must be stopped or the creature must be stopped can not die,
Regeneration (Ex) A creature with this ability is hard to kill. Regeneration creatures heal the damage at a set rate, like a quick healing They can not die while their regeneration is still working (Although creatures with regeneration are still unconscious when their hit points are below 0). Certain types of attack, usually fire and acid, cause the regeneration of a creature to fail in the round following the attack. During this turn, the creature heals no damage and can die normally. The descriptive text of the creature describes the types of damage that cause the regeneration to stop working.
There is an open FAQ request in the Paizo Messageboards, asking if trolls can be killed by deaths or not.
Also note that the Pathfinder version of Regeneration is formulated differently than in version 3.5 (link), which did not mention that they can not die, and that treated things with non-lethal damage instead. While the resolution spell text is mostly the same, including the part that the target becomes dust,
However, you can try to eliminate their regeneration
One thing is certain: they must stop their regeneration, either with the correct type of damage, with something that prevents regeneration, or by removing the regeneration from the creature (by morphing or transferring).
As much as it sounds ridiculous that a bunch of dust can still regenerate, it kills them immediately with a death effect and lets them come back to life a few laps later.
There are many opportunities deactivate they (sleeping, burying, submerging, including their soul in a gemstone), but they do not kill the creature.