Minors usually see to really minor sh, theoretically if it's deep enough to penetrate past the top layer, then it's to be seen at a&e, not minors. If you arrive by ambulance they won't see you for sh, as it's likely to be more serious anyway.
The reasoning is simple, in self harm the physical injury is only part of the issue - it's considered necessary to be seen by people who are able to make sure that you're not in any further danger to yourself at that point, and hopefully put some further support in your direction if required. MIUs cannot provide that extra support, referral or assessment, (wanted or not), and that is why their guidelines are different from minor accident injuries.