Can Byakugan read mind? In episode 46 of Naruto,from 11:57 to 14:05 minutes 
Neji Hyuga went on saying the mental state and thought process of Hinata Hyuga.Although he linked his mind reading with external physical stances,he deduced correctly  the thinking of Hinata.

At 13:29 minutes,Neji even claimed that he can clearly read Hinata's mind.

Is Neji truly reading her mind or is he just logically deducing it?

After that episode,I have never seen any Hyuga reading mind by Byakugan.
Short Answer is: No, Byakugan cannot read anyone's mind. As to the episode that you are referencing, you need to keep few things in mind:

1) Hinata, during the Chunin exams( I think that's what they're called), was very predictible to begin with, and hence any decent ninja would be able to know her next move by looking at her stance.

2) Neji, with his Byakugan, can see Hinata's chakra-flow, and chakra-flow changes depending on the person's physical and mental state.

3) Neji was fighting Hinata, and it is a common tactic to say things to your opponent that will affect their confidence. If you watch the whole fight, once Hinata remembers Naruto and gains confidence, Neji stops bragging about reading her mind.

Also, Byakugan's ability to gain knowledge of person's mental state by reading chakra-flow, is not the same as reading minds because chakra-flow does not indicate anything about one's thoughts.