What is the best way to clean mold off my leather purse without destroying it?

There are a lot of different types of leather cleaners available at various outlets—I would check to make sure you get a gentle one. I know Coach makes one, and also Leatherstuff.com sells one which I think is very popular.

I hear you @Deja_vu. I am in Queensland, Australia and we have never had a mold problem before but I pulled out a leather briefcase this morning… mold. I just brushed it off and then wiped it over but for other places I have been using Oil of Cloves. It was even on my timber blinds. It apparently helps stop the mold returning. Not sure about using that on my leather goods either though.

Lysol spray disinfectant.

You could try Saddle Soap, used for horse tackle. It works on all leather, reconditions it and leaves it smelling fresh. If applied properly, a thin residue will be left that should help hold back the mold.

Make sure everything is properly dry before storing them again, the cupboard itself may need some extra ventilation to help prevent regrowth. For health reasons, it might be as well to clear the cupboard right out and treat it with something to kill that mold, it’s not good to be breathing the stuff!

I would wipe all mold off with a cloth dampened with water and a little vinegar. Wipe dry and leave in the sun for a while.

Then, on all leather surfaces apply Neatsfoot Oil,
or the equally useful MInk oil.

Mink or neatsfoot oils are good for leather (normally used for waterproofing), but because they are both oils they can change the color of the leather, and if there is decorative stitching, it can alter that as well. You cannot use oil on suede without ruining the finish.