Is all of economics reducible to supply and demand?
In market exchange, mostly, with the arguable exception of monopoly price since technically a monopoly capable of setting its price has no demand curve beyond a single point which it sets at any one time. What's more important to the market, however, is understanding what makes those supply and demand curve, and the implications of those curves. Most importantly there are concepts, such as public good, consumer's sovereignty, and business cycle theory which cannot be described by S and D. However, prettymuch the entire market process can be displayed with these graphs... So kind of.
The simplest counter-example is Crusoe economy.
If you're asking whether the price of a good is completely determined by supply and demand, this isn't true. Consider the concept of elasticities.