AmiAmi doesn't do cancellations, but if you contact them through the "Contact Us" link and ask them nicely, they usually cancel stuff for you (just as long as your reason sounds legit and you're genuinely polite about it). Don't let it happen too often though, as they get annoyed by it (it also gets put on their record). It's only regular customers where they cut some slack, but even then that's never a guarantee that they'd casually cancel stuff for you.
Also don't ever wait it out and not pay for the order, AmiAmi hates that even more and they're more likely to blacklist you for it if you do it more than a couple of times. Not that it would ever get to this point, but having them literally close your account is the worst thing that could happen, and it results in them closing any new accounts that might contain your details eg. address, credit card, email etc. (basically you can't register ever again unless you seem like a completely different person with different details)
Hope that helps, I'm actually a fairly regular buyer on AmiAmi and while the site layout, overall selection and prices are great, they can be quite harsh when it comes to continued cancellations (keyword: continued, so just don't let it happen too often and you'll be safe).
. Japan Post hands my packages directly over to USPS, and strangely enough, they've been pretty efficient in delivering them on time.
