It's precisely because your body is incompressible that this happens. Forget for a moment that you have a body and only picture the air-filled spaces that you are carrying down to the bottom of the ocean with you--sinuses, lungs, mask, stomach, intestines, etc. Every one of these air spaces is surrounded by mix of incompressible fluids (water, blood, various bodily fluids, etc.), rigid structures (ribcage, the frame of the mask, the bones of your face, etc.), and semi-rigid tissues (cartilage, skin, etc.).
At sea level, the average person's blood pressure of 120/80 works out to about 1.16 bar absolute. At 60m, this same person has a blood pressure of 7.16 bar absolute. The reason they don't explode in a giant spray of gore is that the surrounding water is pushing in on their entire body with a force of 6 bar. Since blood and most body tissues are incompressible, the net result is that their blood pressure is still 1.16 bar, so the force against the walls of their blood vessels remains unchanged.
The exceptions are where you have blood vessels passing close to air spaces that, for whatever reason, are at a lower relative pressure. This is usually because these air spaces are surrounded by some kind of rigid structure that prevents the air space from being compressed enough to balance the force of the water pressing in from the outside, such as your mask.
So, imagine your blood is pushing against the walls of your blood vessels with a force 7.16 bar (thanks to the water pushing on your body), and the air space inside your mask is only pushing back with a force of 6.16 bar (since the mask can't flex enough to fully compress the air inside). The difference of 1 bar is enough to rupture blood vessels, and generally make a mess of your face.