Keeping it down is easy

Dealing continual damage will keep the Big T down for the count as long as you want to keep it down. Drowning him or placing him in an environment that causes continual damage that he can't resist (or something more exotic - Positive Energy Plane?) can do the same job. Big T can't burrow, so you can drop him in a deep hole (dug with magic, probably) and then cave it in on him.

Making Him Dead, Though...

Essentially you'd need a way to strip him of the regeneration trait entirely. 3.5 had a psuedo-poison (Trollbane) that would suppress Big T's regeneration, but that content isn't available in Pathfinder and furthermore their version of the Big T ignores it by virtue of your quoted text. Without a way to strip the ability entirely the best you can really do is kill him, summon a small army of flying things that don't need to breathe, and ask them to drop him off in the vacuum of space.

And Requested By Comment

Further clarification on the Positive Energy Plane was requested, so:

The Tarrasque is not immune to being blown up by the Positive Energy Plane, though it is immune to dying thereby. Dropping him into the Plane is mostly to get rid of him from your dimension; lacking a native way out, he heals, overheals, and then 'dies', returning to 1 hit point to restart the cycle. The Negative Energy Plane isn't as useful because the Tarrasque regenerates the damage it's dealt every round, and even if it comes into contact with some aspect capable of killing it instantly Big T's Fort save is more than sufficient to protect it.

Countering a specific, known threat as a high level Tier 1 spellcaster is usually easy. This is no exception.

Even without appropriate tactics as suggested by Brian Ballsun-Stanton, there is no reason an epic-level Cleric shouldn't be able to just straight-out tank a pair of mundane warriors.

Fighter incoming? Beat him at his game.

You may have heard that "AC doesn't scale as fast as attack bonuses". Well, that applies to muggles, an epic Cleric really doesn't care.

For instance, the Cleric could have the following:

• Epic Mage Armor. You didn't want the Cleric to have custom epic spells, but this one is stock. If you don't want to spend one of your precious Epic feats on stock Epic Spellcasting, just go with some cheap bracers of armor and make up the difference elsewhere.
• Monk's Belt. I assume the Cleric's Wisdom now cancels out the Fighter's Strength.
• An Animated Shield is cheap.
• Add Magic Vestment to your shield for an instant +5.

Just keep going (Ring of Protection, an Ioun stone, Amulet of Natural Armor if you can combine it with your Periapt of Wisdom) until the desired level of protection is reached. If you don't want the Fighter to hit you, the Fighter just won't.

If you go the AC-pumping route, I'd say the biggest source of concern should be that it makes the mundane party members useless and boring. Don't overdo it.

Sneak attack damage? Fortification.

You may still be scared of a Rogue popping out of some shadow and touch-attack stabbing you in a kidney. An armor or shield of Heavy Fortification means the Rogue's trick doesn't work. At all. No save.

Greater Dispel Magic? There's a thing for that.

Afraid of some uppity mage coming around and target-dispelling a critical buff? You should be, even with your caster level advantage. Which is why I never leave home at high levels without at least one Ring of Counterspells with Greater Dispel Magic in it. (Or a non-core improvement, ahem.)

Regardless, you probably want to have your buffs cast with an active Bead of Karma. That gives the buffs a Dispel DC of at least 38 (11 + CL (23+4)), hard to beat in core with just Greater Dispel Magic (capping at +20).

Just hope they don't think of bringing Disjunction!

Contingency is very good.

You have a Contingency up and running (it didn't get dispelled, see above). In core, a Heal is probably as good as you're going to get. Make sure it is timed (that is, phrased) well!

You might be able to make the attacks exceedingly unlikely to hit by using it to (further) juice up your AC. If you key it to Polymorph (beware of unusable equipment, do your math first!), you could look for a form with high natural armor as the least of its tricks.

Make sure Time Stop goes off.

If you get a Time Stop, the Cleric likely has enough time to get up enough short-duration buffs to survive most things. I consider Spell Stowaway keyed to Time Stop a worthy candidate for an Epic feat.

Now what?

You have done your homework, and have an invulnerable murderous machine of a Cleric. Just make sure your players do have a way of winning. In my experience, high level PCs usually do, but be careful.