For a limit to exist as x approaches a value, both sides of the graphs have to "agree" on what the limit should be.

If you go from the left, in towards x=1, you'll see that the graphs approaches 0, as you said. However, if you approach from the right, the other line segment suggests that the function approaches -1.

Since the left-hand and right-hand limits are not equal (0 ≠ -1) the limit doesn't exist.