I would ask the print shop how they would like the file to be setup. You may not have to do anything. I have worked with some print shops that want you to use a specific spot color or name for the Layer.
You will need to expand both the green background and the layer mask of the image. You can do this with Path Offset or manually move the anchor points. Anything with color does need to go past the trim/cut line.
Example of using path offset for the 2 objects. Make sure to move the bottom of the green background up to the original spot.
Your file could look something like this.
You can save a copy of your artwork as a JPG to show the print shop that there is a cutline. The copy is a JPG proof for the print shop to understand what you're trying to do. You should expect a similar image back from the print shop indicating where the cutline is.