Mitchell, who now lives in Lake Como, Italy, said the Scottish international needs to take responsibility for his actions and not blame “someone else”.
Griffiths will spend time away from football as he bids to recover from “ongoing issues” which have taken their toll on the player in recent months.
Celtic manager Brendan Rodgers gave his striker full backing as he revealed the news on Wednesday afternoon, saying the club will do “everything they can” to help him get better.
Mitchell, who was in charge of the SPL from 1998 to 2002, didn’t share Rodgers’ stance.
He tweeted: “So siring 5 children from 3 different women and a betting/boozing culture isn’t the worst type of classic laddish boor? Miss anything? At some point people need to take responsibilities for their actions in life. It isn’t always the fault of something else. It’s just you, dude.
When asked if he had any heart, Mitchell added: “For pour souls never given a chance in life and beaten down by it every day yes. He is not one. For lucky boys with outlier talent, and earning over £1m a year then, em, no.”