A mutex is just a lock. Like locking on portapotty - ensures that only one person uses it at a time. There are many types of mutual exclusion; for a good overview, you should check out "Operating Systems: Design and Implementation" by Andrew S. Tanenbaum or osdev.org . I’ve never heard of a “split mutex” before, and Google returns nothing. Nevertheless, the term "split" implies that it is divided, and therefore not excluded (several people in portapotty), which is not entirely clear.
Normally, you don’t need to worry about mutexes unless you are designing an operating system or device driver. And the only way to affect performance is that the blocked resource is in great demand by other processes (i.e. there is a large line for portapotty).
If you do not have any mitigating situations, such as SMP, etc., it is better to leave it in the operating system to decide how to handle the mutexes and resources, as it should be on it.
Sorry, I could not help anymore. I don't know anything about "split" mutexes. If this is specific to AIX, you can check out the IBM manuals, otherwise there might be something to find in some IEEE research papers.
UPDATE: with further research, this appears to be an example of general case optimization. The mutex is split into two cases: 1) the general case, when nothing special is required, some security checks or kernel bypass functions called fastpath can be adopted, or 2) we cannot assume that the checks pass or cannot be done by certain optimizations called a slow trajectory. Amdahl's law is often used to quantify this case optimization.