Roughly chop the carrots, celery, and onions. The mixture doesn't need to be perfectly chopped, because you'll puree it later.
Cook the vegetables in a slightly oiled stock pot for few minutes, until the onions are translucent.
Add water until just covering the vegetables, and then add the salt.
Heat the water to a boil. Then reduce the heat, and simmer until the vegetables are tender.
Add tomatoes and mint. Using an immersion blender, blend the mixture until it has the consistency of a rough puree (not completely smooth).
Bring soup back to simmer, then taste and correct seasonings if necessary.