How should I remove tile put down on top of linoleum?

Without seeing your floor, my best guess is that it will be a 2 step process. First use a pry bar to get the tile up and removed. Then see what you have left to deal with as to the linoleum, you might need the pry bar and shovels to get that up too. If it is really glued down and old, I might even consider taking up the sub floor with it and start fresh.

https://www.thisoldhouse.com/how-to/removing-ceramic-tiles

A hammer and a pry bar. Use the same to remove the tile underneath as well.

Put a piece of plywood under them cut to the same size as the cushions

I would get one of those mini jackhammers at a rental place....and definitely invest in the long-handled heavy duty floor scrapers.

http://www.homedepot.com/c/how_to_remove_ceramic_tile_HT_PG_FL

When you get to the vinyl tile use a heat gun and that scraper.

Thx!

. I would think once you get the first tile up the rest should come right up with little effort. Thin-set needs a porous surface to bond with and linoleum is slick. You I would think once you get the first tile up the rest should come right up with little effort. Thin-set needs a porous surface to bond with and linoleum is slick. You should be able to practically sweep it out. The linoleum will be more difficult to remove. You need to see if you can determine what it was glued down with to decide the best removal method. Some have asbestos and would need specific hazmat removal. Google Black Mastic for specs on the various types.