I took some audio classes in university and there are a few factors involved that would make it more or less difficult to mash up two songs. I don’t know what it would cost to pay to have someone do this.
To mash up two songs, you need two different elements of the songs separated; the vocal only track (Acapella) from the first song, and the instrumental only track(s) from the second song. Then you can use audio software to layer the different sounds together. Depending on the popularity of the songs they could be available for download if you hunt around online.
You might also need to adjust the speed of one song to match the beat of the other song, and/or arrange the vocal samples to start playing at a good point in the instrumental track.
If the songs are written in a different key this could also make it sound funny. I think this can be adjusted, but I can’t remember for sure. (I did this years ago.)
There is free software you can use to do this available here: http://audacityteam.org
Cutting out parts or shorting a song is a lot easier to do.
When I used to do my homework in school, I mostly followed tutorials on youtube. There are lots on tutorials there using the free Audacity audio editing software. If you decided to try it and enjoy it, you can get into using sample loops to build your own songs fairly easily.
I just google it and found a beginners mash up tut:
https://www.youtube.com/watch?v=FzlvBxX7gYE
Hope that helps! It would be awesome to have custom songs to dance to!