You might be using the wrong settings.
For paper, most people want to use Engraving, (not cutting). The Engraving will remove a thin line around the cut area. In order to create an engrave on the file…set a slightly wider Stroke and then Expand it into a Filled shape.
The machine can move faster when it engraves, and there is less burning residue on the paper.
The thing to remember is to use faster speeds, and less power.
For the MDF, you will see more burning for tight small curves. You can use paper masking on the MDF to prevent that from darkening the small curved areas. Something like this…paper tape with adhesive.