At 14th level, Stone Sorcerers (from Unearthed Arcana: Sorcerer) get the Stone's Edge feature, which states:
When you cast a spell that deals damage, choose one creature damaged by that spell on the round you cast it.
Does this work with cantrips, or is it exclusive to 'leveled' spells only? Also, if I use booming blade and thunderous smite in one attack, does the Stone's Edge ability stack?
If the feature did not affect Cantrips, it would expressly say so.
Starting at 14th level, your mastery of earth magic allows you to add the force of elemental earth to your spells. When you cast a spell that deals damage, choose one creature damaged by that spell on the round you cast it. That creature takes extra force damage equal to half your sorcerer level. This feature can be used only once per casting of a spell.
—Stone's Edge, Unearthed Arcana: Sorcerer
There's no language stating this damage may only be dealt once per turn, so it must be able to be applied to both spells.
There is no qualifier for the Stone Sorcerer's Stone's Edge so it applies to all spells, both cantrips and level 1+.
The only limits you have from Stone's Edge are:
When you cast a spell that deals damage, choose one creature damaged by that spell on the round you cast it. That creature takes extra force damage equal to half your sorcerer level. This feature can be used only once per casting of a spell.
In this case, you have cast two spells that affect the same creature. You can apply the Stone's Edge to both.
It's unclear what "can be used only once per casting of a spell" means. It's likely that this is protect against Quickening a spell to get it twice, but it's something to consider for other combos you may have in mind.
