20mm deep with a 65mm saw blade won't leave much to clamp, probably be 22mm bore if a metric one and I would say 30mm flange on the arbor would be minimum so only aaround 16mm depth available.
Saws do flex and will try and wander into the first cut, if you must do it with a saw then 1mm down each side of the 4mm slot and then take out the waste with more passes of the same saw or a 3mm one down the middle
Depends how rigid your lathe setup will be, with a coarse tooth blade that has about 24teeth and using the 1mm option you may be OK but the load from a 3mm cut will be similar to parting off 65mm stock so chatter will be likely..