Welcome to the forum!
We can't know whether the file which you showed a screenshot of is proper for cutting, by looking at the raster (PNG) screenshot. We would need to see the SVG file. But I can probably address a couple of things. And ask a couple of questions.
I notice that you have some rather wide strokes on, as far as I can tell, everything except the black object. Do you need those to be cut as separate pieces, from a different color of plastic? I can't tell whether you have those as paths already. But once we can see your SVG file, we can tell you how to make those into paths, if they aren't already.
Next question. Do you need the border of each piece to meet? Or do you want to lay the whole shapes on top of each other, after they are cut? I assume your file is made by having the shapes on top of each other, but I'm guessing that's probably not how you want to cut them. Typically we would expect that you want the borders to meet, so that there is no overlapping of the pieces after they are cut out. But I don't really know your end goal with the plastic pieces. If you need the borders to meet and not overlap, we can tell you how to do that as well.
Oh wait....I just noticed the green oval.... Either it is not whole, or you already have the blue rectangle created in 2 pieces (and the oval is partly underneath the bottom section of the blue rectangle). It's hard to tell, as I've already explained, without the SVG file.
If you're happy with the design, from what I can tell, it looks like it should work for cutting. Well, except for the couple of things I mentioned, which might or might not need to be fixed. If you can answer my questions and share the SVG file, we can give let you know if it needs a little more work. And also tell you how to do it, if you need that info.
Out of curiosity, what is that object in the photo? I can't decide if it's something that exists in the real world, or if it's a 3D rendering of some imaginary thing. The general look and feel reminds me a game I played on my tablet a while ago. While it seems quite real in the JPG, it's nothing I've ever seen before, haha.