Distilled water is pure and it does not contain any minerals, so may not be advisable for drinking. Although laboratory made distilled water is completely pure, industry made water may still contain harmful impurities. Also there is some probability of exosmosis into body tissues which may lead to swelling.
As you said, distilled water is completly out of minerals/ions. The principle of diffusion is that reagents diffuse from high-concentrated to low concentrated places to reach an equilibrium. So normally, ions from the erythrocytes would diffuse into the plasma to reach that equilibrium. However, it is quite difficult for ions to pass the cell membrane which is not the case for water. So what finally happens is that the distilled water wants to dilute the ions in your erythrocytes, passes the cell membrane and the cells explode because they are too full. As consequence, you die because there is no oxygen transport anymore.