The 26-year-old striker was in the Hibernian side thrashed 5-1 by Edinburgh rivals Hearts in the 2012 final and featured the following season when the Easter Road side were dismissed 3-0 by Celtic.
A win over the Dons at the national stadium on May 27 would complete the domestic treble for the Parkhead club in Brendan Rodgers’ first season as boss.
It would also help Griffiths make up for previous disappointments - and quieten some of his taunting Hoops team-mates who already have winners’ medals.
Speaking at the launch of the new Celtic kit which pays tribute to the Lisbon Lions, the team who won the European Cup for the club 50 years ago, the Scotland striker said:
“You want to be involved in cup finals at the end of the season and I am no different, I want to be playing, starting or on the bench.
“I have been to two cup finals before and got humiliated twice so hopefully it is third time lucky.
“I am sick of being tortured by Scott (Brown), Craig (Gordon) and Hendo (Liam Henderson).
“We sit at the front of the bus on away games and coming to home games and they are always winding me up saying, ‘put your hands up if you’ve won the Scottish Cup’ and I am sitting with my hands on my a**e.
“Hopefully it is third time lucky for me. As I say I have been humiliated twice and it wasn’t a nice feeling but I have a great chance this season to go one step further and get that treble.
“We are only one game away from doing that and I think we have a great chance - but we can’t take anything for granted.
“We have a massive game on Saturday (against St Johnstone) and we have to focus on that and put the cup final to the back of our minds.”