There has been speculation Watson could lose the medal after he admitted during an interview with Fox Footy's On the Couch program to taking a substance he believed to be the anti-obesity drug AOD-9604.
The World Anti-Doping Authority has declared AOD-9604 a banned substance, although the Essendon matter is still under investigation.
Mitchell finished tied for second with Richmond's Trent Cotchin in last year's Brownlow count.
He said the prospect of being given the award had been a subject of banter among Hawks players, but that it did not appeal to him.
"This is one of the ones that gets heckled about," Mitchell said on Monday.
"All the boys have been more than happy to give it to me about that for the past few weeks.
"It's certainly not the way you would want to win a Brownlow Medal, is it?
"It's got nothing to do with me…there are so many things, I don't even understand it all – ASADA and WADA, and the AFL Commission.
"There are so many people making decisions on something I've got absolutely no idea about.
"But if you're going to win a Brownlow, that's not the way you want to do it."
Mitchell has polled a combined 56 Brownlow votes in the past two seasons, finishing second both years.
Those votes were all gathered as a midfielder, a role the 30-year-old has not performed as often in 2013.
Instead, he has frequently played at half-back – although that has made him no less prolific.
Mitchell said it was at times frustrating not to be playing in his favourite position, but he was enjoying learning a new role.
"I guess it keeps me on my toes," he said.
"Luke Beveridge, our defensive coach, has tucked me under the wing a little bit, and I'm learning a lot about defensive play.
"Parts of it I've enjoyed, and parts of it I've found frustrating – you like to play in your best position sometimes.
"I'm more than happy to play where the team needs me."
Mitchell is one of several Hawks rotating through different positions this season, which he said gave his team a tactical advantage.
"I guess it makes us a little bit harder from a coaching point of view; coming up against Hawthorn, you're probably not sure what you're going to get," he said.
"And we're not really sure what we're going to get either until Thursday night when the coaches present us with what they think is the best strategy for winning that week."
Mitchell is yet to miss a game this season, and said his body was handling the change in role well.
"There's a lot more physical contact as a midfielder, but when you're playing at half-back you're covering a lot more ground," he said.
"So you pull up a bit differently.
"When you're in the midfield you pull up with sore shoulders and arms and ribs, and when you're at half-back you feel it in your hamstrings and quads and lower back from all the extra running.
"But they're good roles and I've been pulling up fine every week."
