Does the water we sweat come from our blood plasma?

Yes - though not directly; there are normally no openings from the blood stream to the surface! Water leaves the blood stream primarily in the capillariy bed and enters the interstitial space in a passive (not using energy) hydrostatic process, and is then absorbed by cells. read more

Sweat is a liquid that is made by the skin when the body is hot. Sweat is made in sweat glands under the surface of the skin, and it comes out of tiny holes in the skin called pores. Sweat is mostly water, but it also contains some salts. The body makes sweat to cool itself down. read more

The sweat glands in our skin contains two different groups of sweat glands: apocrine sweat glands and merocrine sweat glands. Sweat also helps to remove waste from the body. Perspiration, or sweat, is your body's way of cooling itself, whether that extra heat comes from hardworking muscles or from overstimulated nerves. read more

The fact that sweat is (as Daniel already said) hypotonic to our blood plasma means that the relative level of salt does increase when you start sweating, but not nearly as sharp as it would if you weren't loosing any salt at all during the loss of water. read more