I just started my PhD in physics. It has been 6 months. I have had a mentor for sometime and I have wanted to add him as a co-supervisor. My university told me he cannot be added as a co-supervisor because he works in the same field (physics). The co supervisor can be added only if he's from another discipline like biology for example. Is this how these things work? I am confused and also angry. My supervisor says that I can still collaborate with him. But I still don't feel good about it.
In the US, at least, every university sets its own policies in such things so you need to ask them for reasons if you really want to know.
But a typical reason might be to optimize (in some sense) faculty usage and efforts. Another might be to assure that you don't get conflicting advice. Some questions here relate to problems with co supervisors. In the case of a dispute between "advisors", should it arise, having a single advisor makes it clear whose advice you need to follow and the dispute can't be used to block you. It happens.
And your assumption about funding travel might be erroneous. Funds don't magically appear and if the place doesn't allow co-supervisors they are unlikely to have funding for such.
External supervisors are another issue as they may get no credit for advising you.
That said, you can certainly seek advice from whomever you wish, local or otherwise. A co-supervisor formal relationship is mostly just an administrative acknowledgement, unless funding is supplied.
The exception for cross-discipline co-advisors is likely there to encourage such things, as is appropriate.
But, as your advisor suggests, you can get advice and collaborate with others. The policy doesn't prohibit that.
There is one caveat, however. You say that the prohibition applies to co-advisors in the same discipline, but your definition of that seems very broad. Physics covers a lot of fields. Make sure you understand the policy. Different physicists in different specialties do quite different things. Maybe different enough in your case.
This is very much institution-dependent. Actually in many examples I’m familiar with, the co-supervisor must be a member of the same (graduate) program so a would-be co-supervisor from biology would first have to become adjunct in physics to be granted co-supervision privileges, effectively becoming a member of the graduate department (here of physics) in addition to their regular duties in their home unit.
As a result, “sharing” students between faculty in the same unit, subject to some formal agreement (which may include sharing the funding burden if required) is not that uncommon.
There is really nothing you can do. In my experience units have (usually good) historical reasons for this or that policy, often driven by the desire to rectify some previous abuse or avoid some tricky situation.