you will kill yourself removing the roots. Just mow them for a few
months during the growing season. Or, if you do not wish to spend the
growing season mowing, carefully paint their leaves with a small paint
brush dipped in Roundup (this works well at the height of the growing
season, which is in May around here). Four leaves per bramble usually
kills them. Yes, you can leave the cuttings where they fall, but do not
press them in or cover them with other mulch because they root easily
(so do not put them in pathways or in the compost pile).

You will find that weeds, including brambles, generally do a good job
of conditioning the soil. You will find dark soil underneath, and as
those dead roots in the soil decompose, they will further break the
soil at depth. You can probably plant without tilling, with a light
layer of mulch to prevent weed seeds germination