The saw-leaf cactus belongs to the tropical cacti. Sounds contradictory! This plant is an epiphyte and sits on top of other plants. Therefore, it makes sense that the saw-leaf cactus - like the better known desert cacti - stores water in its leaves, since it cannot absorb water from the soil.
The optimal care is therefore somewhere between a desert cactus and a tropical plant. A lot of bright light without direct midday sun (less light will do, but then you get no flowers and longer shoots) in a very airy substrate and a moderate amount of water are ideal. If you want to get the plant to bloom, put it in a cooler place in winter.
Note: the red leaf tips in the picture are caused by direct sunlight. If you put the plant in the dark, the plant will turn completely green.