Adobe Premiere - Razor Tool screws up clip I'm trying out video editing for the first time and basicly I just want to cut a part of my video.

So I take Razor tool and click on these two blue lines I've drawn with MS Paint:


And now my clip is ruined. When playing or going frame by frame it jumps back and forth.

Like here: 

See that casting bar in video preview? It should be shrinking, but I go few frames ahead and it grows, because video gets back in time: 


How did I manage to screw up so easily? How to correctly cut that part so I could move it/delete it without screwing up whole clip?
The problem is not the razor tool.  You must have slid the contents of the part you razored back in time using one of the other tools.  The easiest way to recover is to undo the edits or to simply drag out the original again.  The razor tool is completely non-destructive, so it hasn't altered your original video at all, just the parts of the video in your sequence no longer line up with the actual time things occurred.  

It's worth noting that as a matter of technique, it's generally preferable to open a source clip in the preview window and use the In and Out points to choose just the part of the clip you want to bring over and then assemble clips together.