what does 'though' means ?

'Though' is a synonim for 'however.' It's short for 'athough.'

Off the cuff...

It indicates that the sentence is an exception to inferences that the reader might make based on previous statements.

eg,

I hate cows. I don't hate this cow, though.

Or, it indicates that the sentence is pointing out a notable fact that puts previous statements into context.

eg,

I hate chicken. I'm a vegetarian, though.

Is the meaning of this sentence the same with
"I hate chicken because I'm a vegetarian" ?

Very similar... But I think is like this :

I hate chicken. But have on mind that I am vegetarian.

Am I right ?

You're right, mirage.

'have on mind' means 'remember' or 'note', right ?
if so, i think using 'but' in this sentence is not appropriate