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Since that's the foundation of your home, I suggest a professional to make sure that it's done properly.
Check the outside of the wall. Before you do anything with the inside, you will have to remove the water seeping in the earth on the outside of the basement wall that is creating this issue. If you don't, you will continue to have a crumbling wall inside as you will just be covering up the real problem.
You’re best bet is to hire a professional who will help you resolve whatever is causing this problem then fix it. Messing with your foundation could cause more problems than you intended.
You are getting water in it somewear
You will need to find out where you are getting water/moisture coming in and go from there!
https://www.bobvila.com/posts/11358-help-basement-walls-are-crumbling
http://www.michiganstonemason.com/crumbling-mortar-in-stone-foundation-walls-and-how-we-fix-it/97/
https://www.reference.com/home-garden/repair-crumbling-cement-walls-fe7b2b2f74132394
https://www.doityourself.com/stry/6-stone-basement-wall-repair-tips