If the preview is jumping around like that, instead of treating it as a single connected design, select everything, un-group it (Ctrl-U) then use the auto-join tool (Edit > Auto Join, or Alt-J) to connect the shapes together.
I would also remove ‘Order by Priority’ and ‘Order by Group’, and turn off ‘Reduce Direction changes’ at least, until you properly understand what they do. Just turning on everything isn’t always the best idea.
As a starting point, skip trying to cut the complex shapes, and start with something simple and known, like a circle and a square, maybe with some simple text, and see how those come out with the settings chosen. From the image of the cut you’ve displayed, it looks like you could have a loose belt or lens, or your acceleration or speed settings could be too aggressive, but since the shape you’re cutting is wobbly to begin with, it’s hard to see what’s from the original shape and what’s erroneous output.