If it is couch grass you will need to laboriously dig out all the roots sing a garden fork and a lot of patience. If it is not couch grass you will probably get away with cutting turves with a spade - cut the width of the spade and then slice underneath and lift off. You can then stack the cupo turf upside down to rot into giood loam or you can bury it upside down in a trench as you move along the row - but make the trench deep enough to have a spades depth of soil on top of the turf if you can - from this depth it doesn't regrow.

If you do not know how to recognise couch grass it is the one with long thick white roots that spread widely under the ground and pop up new plants here and there. YOu do not need any other equipment than a good sharp spade and a garden fork.

Couch grass does respond quite well to glyphosate and as it is so difficult to dig out every piece of root, it may be a better option even if you don't like to spray. As long as it's in an area you haven't planted, the one off effort to remove it is probably worth it. I carefully dug out all my deep beds but left the paths between them, which I covered with mulch, and now the couch grass is as bad as ever invading the beds from the sides!
Once 'cleared' always weed as often as possible to finally give it the 'coup de grace' (perhaps I should say the 'coup de grass!)

I guess you are wanting to remove an old lawn. I like bertiefox have removed sections of lawn. But I use an old spade. I cut 'strips with a lawn edging tool, then cut along the strips so as to make a ladder pattern. I then dug down 2 - 3" with a spade, and then pushing the spade to a horizontal level, I cut the soil below the grass. It is easier to remove in small sections. You can either stack the turves grass to grass and then soil to soil, or put a few in sacks and take to your local tip that takes greens.
Turf cutters to hire are fine for old utility lawns that have been cared for, but for lawns that are old with all sorts of grasses growing in them, I find turf cutters don't go deep enough to cut out the longer roots, which will regrow.

I just cut the strips with a spade.

Thank you so much for your advice! Will try. Back to work. Let you know how i got on next weekend. Thanks