I have at times tossed pears or peaches in with apples when making applesauce, I can't see why you couldn't do the same with mangos if you happen to have them handy. Just make applesauce the regular way and pretend the mangos are apples (use mostly apples, just a little bit of mango)
Any kind of apples you want. I think a mix of more than one kind makes the best applesauce but if you are adding mango it may not matter. If possible, avoid using ones known for keeping their shape when baked (e.g. Spys) as they will take a loooong time to cook down enough for applesauce.
How To Make Applesauce:
Prepare apples as desired (unsprayed apples can be used peel-on if you have a food mill or chinois; anything else should be peeled first; if you have no food mill or chinois, also core them first).
Cut into large chunks.
Put apples in a large heavy-bottomed pot. If they are juicy apples and/or still have wash water clinging to them, do not add any more water. If they are very dry apples, add just maybe 1/8 c of water.
Cover and set over medium-low heat, stirring occasionally (especially at the beginning). Cook until soft and applesauce-y.
If you have a food mill or chinois, run the stuff through it to remove peels/cores/seeds. If you have no food mill or chinois, and have used peeled cored apples instead, you can either leave the applesauce chunky (some people prefer it that way, you should hear my m-i-l on the subject!) or use a potato masher, ricer, or sieve to smooth out the lumps.
I don't add sugar or anything else, but you can if you want (wait til end and taste).