Application of stone veneer over painted wall
Yes, you must remove all the paint.

All the weight of the mortar and stone will be depending not on the mortar bond to the substrate, but on the bond between the thin layer of paint and the substrate. That bond, which was designed to hold only the paint itself, is sure to fail in time.

I have repaired two different situations like this:


thin brick pavers were mortared to painted concrete, which resulted in the pavers (and mortar and paint below that) releasing from the concrete starting one year later. 
thin stones were mortared to painted stucco, with failure timing and mechanism similar to the previous scenario.


In both cases, grit-blasting would have been the appropriate (and ultimately cheaper) treatment.