Why does price drop as a result of increase in supply According to the Law of Supply, if price increases, there is an incentive for producers to produce more, and therefore the quantity supplied increases. However, for an inelastic good, if there is a supply shock and supply significantly increases, why is there a drop in price? Can't the suppliers sell their product at the same or a higher price to increase total revenue?

Low price elasticity of demand, together with fluctuations in supply over short periods of time, creates serious problems for primary commodity producers, because they result in large fluctuations in primary commodity prices, and these also affect producers’ incomes. A good crop resulting in a supply increase leads to lower prices and lower farmers’ revenues. We come, therefore, to the ironic conclusion that a poor crop may be good for farmers because it increases their revenues while a good crop may be bad for them. Can't the farmers sell their product at the same or a higher price to increase total revenue?
You are describing a special (although very important) market where the short-run market supply function is vertical : farmers will attempt to sell whatever they have produced, irrespective of what that will do to the unit price. I am not saying this is not reasonable: many agricultural products are not really storable (or require special infrastructure in order to be stored), and there is certainly increased pressure to sell, compared to other products.

And indeed, in such a case, one can see a "good crop" bringing in lower total revenues, due to relatively inelastic demand. This is after all the core reason why government price subsidies in the agricultural sector (i.e. supplementing the farmer's income to compensate for low market price) is the rule rather than the exception, in virtually all market economies around the world, where very few other final products enjoy price subsidies (and only temporarily, while for the agricultural sector, it is essentially a permanent situation, of course not for all agricultural products). 

Also, as another real-world remark,  it is not uncommon for farmers to withhold and even destroy part of their crop in order to safeguard prices (and thus end up with higher total revenues compared to what they would have get if they have sold all the crop at a lower price).

I am not sure I understand the last sentence/question in your post. In what sense farmers "can" or "cannot", "sell at the same or higher price"? And "same" compared to what?