This may seem a bit basic and I understand how to use the crop tool. But sometimes when I crop an image, then copy and paste what I cropped onto another image, I end up pasting the whole image before I cropped it. I can't figure out why that happens. Is it something to do with the image format?
Hmm... it seems unlikely that image format would be an issue.
Check Fireworks > Preferences > Edit. Under Options, is "Delete objects when cropping" selected? If not, that could explain it.
Otherwise, keep in mind that copying and pasting involves the clipboard, which is an operating system resource. Generally, it works fine, but sometimes things go a bit wrong. That doesn't really explain what's happening in this case; it's just an observation.