Why does anger "cloud the mind"? There are a lot of anecdotes on frustration and anger inhibiting judgement and problem solving. Examples include "anger clouding the mind" in pop culture, or in programming, where a rule of thumb is to walk away from your computer when you're stuck on a problem for more than 20 minutes. 

I'd like to know the physiological reason why the more frustrated or angry a person gets while trying to solve a problem, the less likely the problem gets solved?
It is a biological/chemical response. Once in a stressful situation, you're not supposed to act smart or able to solve a rubik cube, but punch whatever is getting you angry and/or getting the hell out of the place.
The adrenaline, and other stuff, discharge are responsible for
increased blood pressure, heart rate and what-not (Nordqvist, 2013):

Anger is not just a mental state of mind. It triggers an increase in heart rate, blood pressure and levels of adrenaline and noradrenaline. Anger has survival benefits, and forms part of our fight or flight brain response to a perceived threat or harm.
When a human or animal decides to take action to stop or confront a threat, anger usually becomes the predominant feeling and takes over our behavior, cognition and physiology.

Actually, we do get more acute cognitive abilities... though at the expense of others :

The brain shunts blood away from the gut and towards the muscles, in preparation for physical exertion. Heart rate, blood pressure and respiration increase, the body temperature rises and the skin perspires. The mind is sharpened and focused.

Blood is shifted AWAY from the frontal cortex, responsible for nice thoughts (Hanscom, 2014):

When the real or perceived threat persists we feel or are trapped. This, of course, leads to frustration and anger, which causes adrenaline levels to really skyrocket. The result is that your blood supply is shifted largely to the skeletal muscles, which enables you to flee danger. Other effects include:
Decreased blood flow to your brain – especially to the frontal cortex where most thinking occurs.

Spektor, Treister, et al (2011) states in their study that observing anger in others increases analytical problem solving whilst hindering creative problem solving (not really related):

Studies 1 and 2 supported two of our predictions: Observing
another person’s anger influenced observers’ thinking processes,
and the way anger is expressed shaped this effect. Observing anger
hindered the solving of creative problems and enhanced the solv-
ing of analytic problems.