Prepare the chutneys first. You can do this a few days before and store them in the refrigerator too.
For green chutney, grind together mint leaves, coriander leaves, cumin seeds, chaat masala, lemon juice, and rest of ingredients to a smooth paste with water. You can find detailed recipe for green chutney here.
Here are the detailed instructions for sweet date tamarind chutney.
Once you have the chutneys ready and have boiled the potatoes, putting together the bhel puri is a breeze.
To assemble the bhel puri:
Reserve half a cup of sev and add all other ingredients to a wide bowl.
Give it a good mix and taste test to see if the sour vs sweet vs spicy is good and suits your taste. Adjust the ingredients (add more sweet chutney, salt, etc) to make it perfect.
You can serve in paper cones or simple bowls with generous amounts of sev and coriander leaves for garnish.