Beat it by downloading whatever you want at home instead. You'll have better job security that way. Your employer has the right to allow or block whatever they want on their equipment (just as you get to say what goes and what doesn't go on your property), and to fire whomever they want, including people who keep wasting other people's time.
If what you need has some business justification then work with, rather than against, your supervisor to get what you need. If he's preventing you from doing your job then this way any heat will be directed at him, but at the moment you're the troublemaker.
Some places implement P45 security. People who break the rules are given their P45s. (If you're not in the UK that might not make any sense. A P45 is the form your employer gives you when you leave or are kicked out. I think it's known as a pink slip in the US, although I've never fancied wearing one.) So at the moment you're fortunate in that the measures taken against you are technical rather than disciplinary. Sooner or later though your supervisor will be asked why he's not performing, and the only answer he'll be able to give is that he has to keep watching you and blocking the new ways you keep finding to defeat network security.