Remove a cement slab by scoring the surface using a saw with a diamond bit and breaking the slab with a jackhammer or large sledgehammer. If the slab is reinforced with steel, you must cut the steel to release the sections.
If you do not own a cement cutting saw, you can likely rent one at a tool rental store. Mark a grid on the concrete using a chalk line so it resembles a large tic-tac-toe board. Set the saw blade to cut into the slab and begin the process of cutting the score lines.
After cutting all the lines, begin breaking away the concrete. On large jobs, you are likely to find renting a jackhammer worthwhile. Breaking concrete with a sledge or jackhammer is labor intensive, so take frequent breaks and drink water so you remain hydrated.
Use a large pry bar between the breaks to lift the concrete sections from the slab. Cut any steel reinforcements using a hammer and cold chisel or a hacksaw. Continue the process until you remove the entire slab.
Dispose of the concrete at a landfill. Many landfills have special sections for disposal of this type of material. If you do not have a truck for hauling the waste, contact the local waste removal service about renting a dumpster for concrete waste.