For cutting there should exist exactly those paths that the cutter should slash along. Remove the extra paths. Select your extra line and press DEL. It should vanish and the 2 nodes, too.
If you're already succeeded to split your shape to 2 adjacent, but separate parts, this does not work. You must combine those parts again to one or (a more sure way) load from file your previous version that you know not having any obscure faults. If you're a beginner, you should save often and change the filename, too to keep possible to return back.
Hopefully you work in the same layer where your shape is. If not, then go into it.
You have the right tool selected. This is the curve editing tool. Hover the cursor over a curve, you see, when you are near enough - there is an indicator symbol (tilde).
If you press the mouse button and move the cursor, the curve moves, but the change is in the nearest old nodes. If you double click on the curve, you create a new node. That can be moved and its Bezier handles can be adjusted.
Do not kill an unwanted node by DEL because the result may be quite unexpected. You kill a piece of the curve, too and replace it with one drawn between the adjacent nodes with their old handle settings.
Double click on the unwanted node to remove it and have the curve otherwise as unchanged as possible. The handles in the adjacent nodes adapt intelligently.