We just did this! We found by cutting the vinyl in strips with a razor, we could get a putty knife wedged under a piece and then pull with our hands using pliers. We were stuck with glue underneath but it was okay for the type of flooring wewent with. Good luck!!!!

If there is a thin underlayment, you can remove this, too, if you wish. It may be, for example, 5 mm thick luan plywood. This will likely be stapled down in a million places. You can set your circular saw to be the depth that will just barely cut though the underlayment. Then cut a grid into the floor, about 1.5 ft. on a side. You can then pull up the underlayment and vinyl in one piece. You then need to pull the staples out by hand with a pair of pliers.

Look at youtube videos for "removing vinyl floor" or "removing linoleum floor."

Do you know how old the floor is? If there is any chance of asbestos, which was commonly used in vinyl tile and mastic, you should learn how to deal with it or have a pro do it.

I forgot to mention that this is on a concrete slab.

I think the floor is less than 20 years old.

I guess we're in for a tedious task--not unlike stripping wallpaper (we've done a lot of that too)

I have not tried these myself, but they make scraper blades for a reciprocating saw now. May just do the trick:

Here is a link that might be useful: Spyder scraper

Doing this right now - 4 hours yesterday!! Mine is not coming up easily. Mine is on a slab and I am finding some areas I can get up in decent size pieces (up to 1 ft by 2 ft), others there seems to be so much more adhesive and I am down on the floor with a hammer and nice sharp wide wood chisel turned upside down.

I have a hand tool like the attachment on the photo above and I bent the heck out of it working on my floor and slab so I switched to a wood chisel.

I go after everything first with the long handled scrapper (bully tool) and then I get down on the floor and chisel up what won't come up.

Then I am wetting the slab, letting it sit for a bit and doing another scrape of the left over adhesive. You will want to do this step because if it comes up with water, it will loosen with your water based thinset for the tile and you could have some areas where your tile doesn't adhere well to the slab.

It is a lot like removing wallpaper on my slab!! And takes a lot of elbow grease (as well as a bruised left hand from getting tired and missing with the hammer on the chisel!!)

I have heard you can heat it with a heat gun to loosen the adhesive and then pull it up easier. I opted not to do that because I really didn't want to worry about fumes from heated vinyl/adhesive.

That spyder scraper looks like the perfect tool for that kind of job!

Have you tried softening it with a heat gun?

Update--
We rented a power floor scraper. It worked well to remove the top (plastic) layer, and now we are left with a paperlike layer glued to the concrete. Everyone I've spoken to about this project says wet it and scrape with a floor scraper or flat hoe. This is going to take a while......

I would have thought that it would succumb to heat better than water.

We discovered that my steam mop really helps to loosen the paper/adhesive for easier scraping. We still have quite a task ahead of us....