My love of mashups comes from my migration between DJing (when I love to blend one song right into another on the dancefloor, or follow up a current song with the song that sampled or inspired the track to educate the drunken masses)... and when I started playing live again 10-12 years ago after many years off.
If I didn't know a song, or was learning a song, or wanted to play a snippet of a song that I was working on, I would mash a couple similar ones together or (usually on the fly without warning my bandmates) switch to the other song that was "close enough" that they could keep on playing whatever they were and I would play this other song over the top of the same chord progression. Later it became what I refer to as "dog pill in cheese" where I take one of my favorite nuggets of a song and book end it with something more familiar to the masses.
Elise Trouw does this perfectly by using one of my all time favorite songs by Bobby Caldwell and putting a modern swing on it by adding some Foo Fighters... and if I remember correctly, she adds some Police in there as well. She's great!