I think you're playing the Psycho the way he's meant to be played, but part of it is knowing when to start rampaging. The key here is whether you can kill an enemy shortly after entering Buzz Axe Rampage. If you're at low health while rampaging and can't get a kill, you might not be able to survive, so make sure you don't wait until your health is too low to start rampaging. However, this changes completely once Krieg learns Release the Beast (more on that below).
Looking at your build, Silence the Voices could be a source of trouble as it causes Krieg to occasionally attack himself on melee. This skill is a bit more useful at higher levels when you can put more skill points into it, so you might want to consider consider respeccing to remove this skill for now. (My current Mania Psycho build, level 32, does not have a point specced in this skill.)
Also, once you reach 31st level, the Psycho gets a lot more powerful with Release the Beast. At that point, you can go all-in, then rampage once you reach critical health without much fear. Until then, a Mania build may be hard to do well and could prove too risky. I personally used a Hellborn build until I reached level 31.
However, you haven't described precisely when you're running into trouble. Is it with large groups of weaker enemies? Is it with fewer but stronger enemies? What types of enemies (e.g. bullymongs, bandits, Hyperion robots, etc.) are giving you trouble? Are there specific locations where Krieg's dying often? I can help you better if you provide more detailed information about what's causing your Psycho to die a lot.