I am a beginner, please help me

This is supposed to be a packaging box?

You might not want to use Image Trace on your raster image, because it could become inprecise. This is something you would need to try out.

After Image Tracing you need to expand the result before you get actual paths. But then you probably also need to delete the inside lines which should not be cut. 

Gabor,

Based on a second reading, I believe you may have used Live Trace, and that has turned the thick outer  line into a filled Compound Path which is then cut out, and instead you wish to cut the whole cat out in one piece including the thick outer line, in other words a cut that follows the outer rim?

If that is the case, you can:

1)) Copy the Compound Outer Path, then hide all the artwork except for the copy;

2)) Select the copy Compound Outer Path and switch from Fill to Stroke so you can see what yuou are doing;

3)) Delete the inner path so you are left with only the outer path; this is your outer rim path;

4)) Give the outer rim path the Stroke Weight/Colour or whichever properties needed for your cutting machine.

I am unsure how you wish to treat the smaller thick non compound paths.

Hi ​@Gabor22773582n1bc,

For everything that you want as a cut path, you’ll need it to be a single path (stroke) - not a fill. Your blue lines need a stroke colour applied so you can see them.

Gabor,

How did you (try to) create the SVG, the photo you start with being a raster image?