There are plenty of companies offering a day-tour of Chiang Rai from Chiang Mai, but I wouldn’t recommend those as you’ll
You can either visit Mae Sai as an excursion from Chiang Rai, or you can go direct from Chiang Mai, but you’ll have to pass through Chiang Rai either way.
If you’re looking for a shorter day-trip from Chiang Mai, my top pick is the San Kamphaeng Hot Springs (which are actually in Mae On District, not Sankamphaeng District).
If you want to spend longer at the hot springs, you can soak in the mineral pool – a swimming pool which they pump the mineral water from the hot springs into.