Oops. Hard to understand why Mamaki manages FC like this way. It's really free for Mimaki's cutter users and their website just have trial version for download?????!!!!
i never had any experience with fine cut, but you and mimaki have yo follow the software agreement with finecut. you can try contacting them and making a "media replacement request" for lost or damaged disk. for can then offer to provide an "affidavit of destruction" which often satisfies the EULA. software agreements often restrict the wayba manufacturer can distribute software and drivers (hp is a prime example, carly fiarina thought she was saving money while she tried to single handedly destroy hp)
again, no experience with mimaki or finecut, but i have done this MANY times with other manufacturers and software companies. give this approach a try, be ready with product key and possibly machine serial number. (is your machine registered to you on the website?)