It would be helpful to give the actual size of this cross, and what material it is made out of. Of course any 'provenance' would also be helpful.
Not knowing the size, it's a little hard and from the pictures it's hard to say whether the three marks on the 1st picture are cuts or ridges. The one on the left definitely looks like a cut but the one on the other looks like ridges.If they are ridges, possibly they were were a corpus was attached to the cross with glue to make a "Resurrix" type cross.the ones on the backside could be due to mishandling. They look like cuts and possibly the cross got scratched when cutting away bubble wrap?
My guess is that it is a prisoner's cross, carved from a piece of nearby rock or tile and the cuts are a way of marking time
Guess: Benedictine or Fransciscan