Blood is pushed out of a wound because the blood pressure that the heart creates is greater than the pressure outside the body. Increasing atmospheric pressure would slow the bleeding, and enough pressure would stop it altogether, but it's not that simple.
The effects of high pressure on the human body, whether it's submerged in gas or liquid, are basically the same. Those effects can be serious, and are often fatal. Because divers have to deal with these issues routinely, a lot of easily understood information is available on the subject.
The basic problem is the way chemicals inside the body, primarily oxygen and nitrogen, react to the pressure. Oxygen becomes toxic, and nitrogen causes an effect similar to drunkenness from alcohol, known as the Rapture of the Deep.
Rapid changes in pressure also causes serious issues, even where the pressures involved would not have caused problems otherwise. For example, rapid depressurisation can cause the well known effect that divers call the Bends.
The effects mentioned here are all macroscopic, involving the entire body being under abnormal pressure. If you could localise the pressure around a wound, these issues may not be relevant.