In some of the GNRI/NCC loco guides that I bought recently, these mention that some of the engines were auctioned off after being withdrawn from service; presumably private scrap contractors then moved in to start cutting work, but the guides don't say which contractors were involved.
I think CIE were different, and - being a State body - kept almost all scrapping work "in house", although I have read in some cases that the Hammond Lane Metal company in Dublin did dispose of some railway items, including the former Glenties line bridge at Stranorlar.
In the case of the CDRJC, stock was auctioned off to private bidders (including scrap dealers) after closure. What is interesting is what happened to no.4 Erne, left at Letterkenny after being used to lift the S&L line into there. Like much other stock, Dr. Cox successfully bid for her but had no money to cover the shipping to the US. Erne is written down as having been cut up "surreptitiously" either in 1967 or 1969, but the question is: who did it?