If the mouth has enzymes to digest starch, what are the functions of other enzymes in the digestive tract?
Stomach: pepsin breaks down protein
Pancreas: amylase breaks down starches, trypsin breaks down protein, and lipase breaks down fats
So you've already mentioned salivary amylase, which is secreted from the salivary glands to begin the breakdown of starches. But just know that the digestion of starch does not end there.
When food gets to the stomach, pepsinogen, an inactive protease secreted by chief cells in the stomach tissue, is secreted and then activated by the stomach acid. Pepsin serves to break down protein into polypeptide chains. It also serves to free up crucial vitamins such as vitamin B12.
After the partially digested food enters the intestine, the pancreas secretes several digestive enzymes to completely break down everything else:
Pancreatic amylase continues where salivary amylase left and finishes breaking down any remaining starches.
Pancreatic proteases, such as trypsin and chymotrypsin, pick up where pepsin left off and break down the polypeptides into individual amino acids.
And pancreatic lipase breaks down the fat. Note that the bile is extremely important to this process, because without it, the fat is not properly solvated and the lipases cannot break it down as effectively.
After that, the individual sugars, amino acids, and fatty acids are absorbed in the small intestine, but that is a story for another time!
Hope this helps!