So technically you could play around with the copy you have and change certain parts of it.You have purchased it you now own the film it is no longer the distributor because it is solid you own copy
As I understand it, there's probably no law to prevent you from ripping pages out of your own copy of a book, sellotaping them back in in the wrong order and drawing moustaches on all the ilustrated characters with a felt tip pen as long as you're only using your tampered copy of the book for your own private reading. So presumably, on the same basis, the copyright law also wouldn't prevent you from mucking about with your own particular copy of a DVD, eg: scratching out scenes, redubbing the soundtrack, again as long as you were only using your vandalised DVD for your own private viewing.
What you're obviously not allowed to do is to publicly show, distribute, re-publish or post online your tampered book or DVD, regardless of whether you're doing so for free or for money. That would be infringing the rights of the author/filmmaker/copyright-holder to have their work published or shown in the form they wanted. You've bought a copy of a DVD, which as you say is your own solid copy; but you only own that copy of the DVD. You haven't bought the copyright or the adaptation rights on the content. Even assuming that the author or film producers wanted to sell or licence you those rights, it would typically cost you much much more than what you'd pay for your own copy of a book or DVD.
To take a real example, a few years ago, there was a Mormon video rental store in the USA who were re-editing video cassettes of movies such as James Bond films, taking out any swearing, drinking, violence, nudity, etc, and renting them out as family-safe versions of the films. Not surprisingly, the film studios came down hard on them to stop this practice. Obviously there'd have been nothing to stop the store owner from fast-forwarding or deleting the offending scenes in his own home when showing his own copy of a video to his family, nor anything to stop his customers buying their own copies of videos and doing the same for private family viewing. It was the distributing
of his tampered versions that was the criminal offence.Edit:
I see that as I was writing the above, Jock's posted a similar, if more succinct answer. Oh, well, now you've got two answers!