Popular MIDI files are usually pretty easy to find with a simple Google search. If the songs that you want do not come up quickly then you will be really struggling to get them anywhere as there’s relatively few people still producing MIDI versions of songs.
One of the big problems with trying to find MIDI files, is that the quality of MIDI programming is very variable. A lot of public domain MIDI files are very poor.
An alternative approach would be to see if you can find the sheet music, then copy the parts into a MIDI sequencer. A few sequencer programs even have OCR for sheet music (for example “Sibelius”).
Some posters on the forum have likened it to taking the chocolate out of a chocolate cake or the milk out of a cup of tea/coffee.
Once the tracks have been mixed down ito a stero pair it can be next to impossible and would still be even with the biggest super-computer in the world. The grownups in the recording studio do it by employing multi-track recording - one track per voice and per instrument and later mix it down for production use. It’s only if you have access to those master recordings that you can un-pick the mix.
Update: sometimes it is possible to buy ready-made studio-produced karaoke versions of songs with the vocals missing. It could be worth a little web surfing to see if you can find what you need …