why dead mouse doesn't bleed when we cut their skin?
From personal experience, extracting organs/tissues of over 1000 mice I can give some hints:
Mice blood coagulates quite fast after death. If you need to extract blood, you are under time-pressure and many scientists extract the blood directly after death from the heart using a syringe. If you are not fast, you miss the chance of drawing blood as this can't be done after coagulation. Others cut up the thorax (post mortem) and then directly draw blood with a syringe. I personally never tried this technique but I spectated that mice bleed a bit, directly after death, when opening the thorax, however it's not much.
After drawing all blood from the heart, mice don't bleed, no matter where you cut, potentially because of low blood content remaining. (Un-?) Fortunately, I never had to cut mice that were alive.. so I cannot tell you what would happen if they were alive.
Edit: Also, in theory, the smaller an animal is, the higher becomes the diffusion/volume ratio and surface-tension/volume ratio. This means smaller animals need less active blood circulation and and their blood vessels might have a small diameter, so that most blood would be kept inside by surface tension if these vessels were cut.
Edit due to comment:
The extractable blood from mice is around 1.5 ml, and I have seen opening of the thorax within seconds post mortem with minor bleeding. Afterwards, the majority of blood (1.5 ml) was extracted directly from heart with a syringe. As this was post motrem, I cannot exclude the possibility that coagulation of blood in small peripheral vesicles already affected the observation or how heart beating would affect it. I cannot say what would happen in live mice and I am happy that I don't have this knowledge.