I read about bitmixer but it's pretty expensive to mix the coins there specially if you are mixing big amounts of bitcoins.
Is there any reliable free bitcoin mixer? Can't i just deposit my bitcoins to exchange and then transfer it to another exchange and then withdraw to another wallet.This way won't i recieve new bitcoins?
you can do that, of course. but if you're looking for privacy that may be not a good idea because the exchange still knows where the coins came from and where they goes.
let me quote something from bitmixer:
All exchanges require the user to scan ID documents, and large transactions must be reported to the proper governmental authority. When you use Bitcoin to pay for goods and services, you will of course need to provide your name and address to the seller for delivery purposes.
This means that a third party with an interest in tracking your activities can use your visible balance and ID information as a basis from which to track your future transactions or to study previous activity. In short, you have compromised your security and privacy.