But if your engine fails at V1 on the runway and your "positive climb" is 0.1% and the runway is sloping up at 0.2%, you cannot get airborne.
Not quite right. The first segment starts at a point known as "reference zero", which is at 35' above the runway and where the takeoff is deemed to have ended - it does not start on the runway.
If the TODA for the runway was greater than or equal to the TODR from your performance calculations, then you are "guaranteed" to get airborne, having lost an engine at V1, and be at 35' before the start of the (rising) obstacle surface at the end of the clearway. This is the point where the first segment starts.
But from there on, there is no guarantee you won't collide with obstacles. It all depends on your first and second segment performance and the slope of the obstacle surfaces over which you are flying.