Welcome to the forum!
Can you clarify what you want to cut, regarding the pattern? The pattern looks like lines or paths, as opposed to closed shapes. So I'm not sure if you want to cut around the lines, so that all is left is the lines, or if you want the lines to be essentially....well, not exactly holes, but slits in the material?
Also, we can't tell from the PNG you shared, whether you've used a Pattern Fill, or whether you're using "pattern" in it's general definition, and the pattern is already made of paths. If you could share the SVG file, we could do more than guess.
As far as I understand the destructive clip extension, it's sort of a shortcut. Instead of using a path operation to get rid of the otherwise "hidden" or clipped away content, the destructive clip does it. (I don't know exactly how it works. For all I know, the extension actually does use a path operation.) So assuming the extension will work on your particular contents, it still would only affect the outer boundary. It would have nothing to do with the pattern on the inside, or with being able to cut the pattern.
I think Moini's suggestion is reasonable. I might do it slightly differently, but only because of personal preference. I'd be glad to go into detail, but I need to understand what kind of results you want for the pattern. And also how you've made the pattern.