Crash: Mind Over Mutant has very linear gameplay. After the intro which explains that Dr. Cortex is back and trying to take over everything again, you are taken to the World screen. You first select the area and then the level. Each area consists of several different parts and the game is side-scrolling. Crash starts at one end and has to jump over pits and avoid enemies to get to the other end. After a few parts, you'll get a check point. If you fail after that point, then you'll start back at that check point.
There are a few different ways that you can die. The quickest is to fall off of a cliff. Sometimes, however, you're going to want to jump down there anyway. If you don't, then you won't find all the hidden things like more mojo. Mojo is used to get extra power for a temporary time and to upgrade the mutants that you have jacked. To apply the mojo towards the mutant upgrades, simply collect the mojo while you are controlling the mutant. You can also apply the mojo Crash has collected by tapping the mojo button in the middle of the touch screen while you are controlling the mutant.
The other way you can die is to lose all your hit points as Crash. You lose points when you get hit by enemies. If you're controlling the mutant, then it will take away from the mutant's hit points instead of Crash's. When your mutant loses all its hit points, then it just dies and Crash is on his own until he jacks another mutant.
After you beat a level, it will open up another one for you. Continue this pattern until you get to the boss of that area. After you beat the boss, another area will be opened up for you. It doesn't really feel like these areas or the enemies have much to do with the storyline, though. There are also mini-games that you can play after you unlock them. They will show up on the World map as an orange star. These mini-games can provide a nice break from the Story mode.