Well, one can still think of it causally - you can still draw a graph with arrows, at least. But it's atypical causality.

Typical causality is like kicking a ball. The ball sits still until you kick it, and you can kick it however you like and it will roll away. But once you have loops, it's like if the ball had to go through a portal to the past and kick itself. As soon as you try to kick the ball, the ball you would have kicked has already gone back to the past and hit itself in a way consistent with the motion of your foot, so it will feel quite unlike kicking the first ball. And in fact it is physically impossible to move your foot in a way inconsistent with the ball being the cause of its own motion, even though trying to kick the ball restricts the possibilities - or rather, being able to try to kick the ball tells you that the possibilities were already restricted...

In typical causality, the ball has a reason for moving the way it does - you can trace the motion backwards to some acceptable starting point, like "I kicked it as hard as I could toward the fence." When you add cycles, tracing the chain of arrows back does not need to end at anything you find remotely satisfactory or even unique - "the ball moved because it hit itself because it moved because it hit itself..."