Paradox vs Tautology. The expression(~p or p )is a Tautology.
Consider this statement(p): This statement is false.
Now here, Statement p is paradoxical.
My question is :- Can we define paradoxes like this as statements which prove Tautologies wrong?

A statement can be provable or not provable, and it can be sound (something we expect to be true, like 1+1=2) or unsound (we expect it to be false, like 1+1=3).
A paradox arises when a statement is unsound but provable.  It indicates an error in the logic.  
The claim of the speaker in the liar's paradox is clearly unsound: it contradicts itself.  But we have no reason to believe it is provable.  So it only has 1 of the 2 qualifications needed to be a paradox.

Can we define paradoxes like this as statements which prove Tautologies wrong?

No.  A paradox isn't only defined by what it proves (unsound claims) , but by the fact that the statement itself is provable.
