I don't know what other line of products Beats may have, but the one in question I assume are the consumer-grade ones. Having that said, absolutely not--you should never mix with consumer grade headphones, let alone Beats.

Consumer grade headphones are designed to make the playback sound better, not portray the playback accurately. As striving professionals, we should be using equipment that portrays the playback as accurate as possible. A while back, I bought ATH-M50's to mix with because they were the only studio headphones I could afford, but ATH-M50's are for tracking, not for mixing. When I switched to DT-880's, I noticed a lot of stray things I never noticed in my mixes before. This would occur more when I would visit a professional studio with NS10's and HS8's with a treated room and sound absorbing environment.

Imagine mixing on Apple earphones. That's like trying to paint in the dark.

lol, you don't get it don't you ? it's all about the matter of perception
if you listen on your beats all the time, you then understand how sound A sounded like, so you can use beats to replicate sound A
even Aleksander Vinter (Savant) used to use Beats before buying any sort of monitor

ultimately, it doesn't matter~

i didnt read the whole thread here, but i def check out my songs on beats by dre (amongst others) cuz also on those headphones shit needs to sound fire - its what a lot of customers use to listen to your music

Yea they really have their own added color to them. Its good to know how your final mix is going to sound on Beats tho being that a good population of the earth probably own a pair.

honestly it doesn't matter what you mix on (ok it kinda does but not as much as everyone says) as long as you know your equipment inside and out you'll have great mixes.  also, reference a ton