How does Slime coagulate and seal holes in tires? How do tire tube sealants like Slime coagulate and seal holes?

They can't coagulate like blood, because there's air already in the tube and they'd solidify. It also can't be in contact with moisture as there's a lot of moisture in tubes as well.

What's their sealing mechanism?
Most sealants work because they are actually a fibrous fluid or rubber solution.  When a puncture happens and the air pressure forces the fluid out a hole, the fibers create a plug or the rubber hardens.

http://www.velonews.com/2010/01/news/cyclocross/technical-faq-tire-sealants_102346