An idiom might be to
Fall on one's sword
fall on (one's) sword
To accept the responsibility or blame for a problem or mistake. Likened to the former practice of a soldier using his sword to take his own life for such a misdeed.
The CEO fell on his sword when widespread corruption in the company was exposed.
While the notion is more at taking responsibility for a problem, it would fit if Francis was intending for Peter to harm himself because of a misdeed.
Francis (placing the razor in Peter's sight): You need to fall on your sword.
Run me through
While TFD and other sources like Grammarist cite Ancient Rome, the Old Testament has this story about King Saul when he was mortally wounded.
Saul said to his armor-bearer, “Draw your sword and run me through, or these uncircumcised fellows will come and run me through and abuse me.” But his armor-bearer was terrified and would not do it; so Saul took his own sword and fell on it.
(1 Samuel 31:4, NIV)
Here is the likely origin story for "falling on your own sword." While Saul's suicide is the ultimate in Saul's self-harm, he asks his armor-bearer to "run me through." It is archaic.
Francis (placing the razor in Peter's sight): Peter, you need to run yourself through.
A slang idiom from Urban Dictionary is to off yourself.
Killing yourself, committing suicide
"dude you are so lame, you need to off yourself"
Francis (placing the razor in Peter's sight): Peter, you need to off yourself.