I'm not looking for the combinations to all the spells or a list for them, there is already a thread for that, I'm looking for a list of what the Wizard spells actually do.

Here are the ones I have used and can confirm some of what they do:

Growth -Causes resource nodes around the wizard to reappear, I can confirm that it affects plants, and the text of it suggest that it should also affect mining.
Spirit Thief -gives the wizard a soul fragment, gives the target a negative focus moodlet. I can't remember how much it decreases and how long it lasts, I want to say it was -15 and 24 hours but I could be wrong.
Teleport - does what the name says, teleports the wizard from one spot to another, uses a fair ammount of energy.
Beacon of Hope - gives a +40 focus moodlet for 24 hours. text suggests that it might give immunity to failing responsibilities but I can not confirm that.

Heal(ing) - Cures light wounds and restores health as far as i can tell, don't know about serious wounds, maybe you need to cast a few heal spells

oh and you can cast this onto yourself as well as on other sims