Just because your parents seemed to make a joke out of it, doesn't mean if you told them, they'd do it then. It could have been an uncomfortable laugh because he didn't know what to say or they just might not have realised that it would upset you. If you feel that you can, you should talk to them but maybe mention that because your friend cut, you know that it's serious and don't view it as a joke so when they made a joke of it, you didn't appreciate it so they know and hopefully won't do it in the future.
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