Why do American supermarkets only carry lamb and not mutton?
It's not just American supermarkets that rarely carry mutton, this situation is similar across the Anglosphere, and I suspect most Western countries too (or at least those without a strong mutton culture). The reason is largely economic. Mutton is expensive and not as tasty as lamb.


First, the immediate reason is that nobody really eats mutton anymore. Yes, there are certain locales, cultures and movements still eating mutton or are trying to bring it back, but today, on aggregate, the demand for mutton is near zero. According to the USDA:


  The U.S. market for lamb and mutton has weakened throughout the decades. Since the 1960s, per capita consumption has dropped from nearly 5 pounds to just about 1 pound. This drop is due in part to declining acceptance of lamb from a growing segment of the population, as well as competition from other meats, such as poultry, pork, and beef. Most meat is sold as lamb and comes from animals under 14 months old.


Here's a per-capita consumption graph:



If nobody buys mutton, supermarkets don't sell them. The supply chain for meats is pretty complex; it's not something that a store manager can just decide one day to order a batch and shelve to see if it sells. Meat needs to be slaughtered and deboned in an abattoir, butchered either in store butcheries or at centres (unless you fancy buying an entire, 50kg cut), and displayed in refrigerated sections. If there's enough local demand for mutton then maybe individual supermarkets can carry them, just as meats like rabbit, duck or kangaroo is sometimes sold at a few supermarkets.
But why don't people eat mutton? People just don't like it. It is an inferior good.


  Mutton comes from older animals and is often less expensive but less desirable to consumers. (USDA)


.


  As can be seen, the average income elasticities across the studies are 0.77 for
  beef, 0.24 for lamb, -0.65 for mutton, 0.47 for chicken and 0.48 for pork.


(Negative income inelasticity = inferior good) That is, as incomes grow, as they have over this timeframe, people want to buy less of it.
Lamb is a superior substitute for mutton. Anecdotally, compared to lamb, mutton is gamier, tougher, and harder to cook. Economically, lamb and mutton have high cross-price elasticity - if one's price grows, demand shifts to the other, indicating that they are substitutes. And the real killer is...
Mutton prices have grown faster than lamb.



Mutton is still cheaper than lamb, but in relative terms it has become more economic to raise and sell lamb. There are multiple market forces at play: the cost of raising the sheep past lamb age, the efficiency of raising lambs (i.e. increased lamb weight), the growth of dairy leading to higher beef supply, the relative decline in wool reducing mutton supply and so on. You'll have to ask a farmer.


Source: Changing Pattern of Meat Consumption in Australia by Lucille Wong, E A Selvanathan and Saroja Selvanathan

Update: didn't notice that the graph was price indices and not actual prices