Vein grafting...

after grafting using saphenous vein, what happens to that vein now that a part of it has been cut?

Well I’m not sure if this is what is technically correct and if this is what you require an answer to but here is my comment:
I had a bypass op 5+ years ago and this vein was used to replace blocked arteries ( it was cut into 3 pieces ) and now the result is what I liken to a motorway which is closed and all traffic has to find its own way round secondary routes as it is no longer available.
So during the day there are ‘traffic jams’ and the fluid in my leg builds up.
During the night I sleep with leg raised slightly (pillow at both ends of bed!) and in the morning the leg is back to normal size.
I’ve lived with this and it’s a small price to pay for an extra 5+ years of living!
Hope this helps
Roy