When removing a tile floor, use a hammer to hit each tile in the center. Remove the pieces carefully, as their edges may be very sharp. Remove the rest of the pieces by inserting a chisel in the line between two tiles and chipping them out. Remove the adhesive from the floor using a floor scraper and if mortar was used as an adhesive, break it up using a hammer, and remove the pieces with a scraper.
If these steps don't help to remove all of the mortar, consider replacing the underlayment. If the adhesive is not mortar but it's still difficult to remove, try to soften it using a heat gun. After that, remove the adhesive using a wide putty knife.
To remove linoleum floor, cut it into strips with a knife, as it is easier to remove linoleum one piece at a time. Heating up linoleum makes its removal much easier, so use a heat gun or a hair dryer. Lift up the edges of the linoleum using a knife, and pull them away from the floor. If there is a lot of underlayment left on the floor, remove a small piece of it and have it tested for asbestos. This chemical is dangerous to inhale, so hire a professional to remove any underlayment that contains it.