Colin, according to your tags, it sounds like you're wanting to remove the paint off the brick walls on the outside of your house.
Anyway you do it, it's going to be messy. Do you want to remove the paint off all the brick or only where you want to repoint the mortar? Either way, I would use a pressure washer, since you mentioned the paint is already peeling. The pressurized water will be able to get under/behind the paint and separate it from the brick facade. that's where the mess comes in because pieces of paint will most likely go everywhere. I would start off with lower pressures, gradually increasing it until it starts removing the paint. Hold the wand at a shallow angle to the brick to best get behind the paint. this will also reduce the amount of pressure being applied to the brick. too much water pressure might damage the brick and mortar. I've seen concrete drives/sidewalks damaged being cleaned with too much water pressure.
If you don't like that idea, then you might try spraying a solution of muriatic acid and water on the brick wall with a pump sprayer. Follow the directions on the label and first test on a small area to check for effectiveness and if there's any discoloration. Muriactic acid is fairly inexpensive and readily available at most hardware and home improvement stores- maybe even walmart? Of course, use the appropriate PPE and protect any vegetation you want to keep. You apply the acid solution, let it work, maybe even help it with a metal brush, and then rinse it off with a lot of clean water. this is a must. You can gradually increase the strength of the solution, if needed. just depends on what kind of initial results you get.
After thinking about it, the pressure would probably be the same regardless of the angle of attack. It's the distance between the end of the wand and the brick that will affect/reduce the pressure.