Derivation of cut rule in sequent calculus I searched internet but could not find any good weblink which shows how the cut rule for sequent calculus can be derived.

I found this paper but it uses implication elimination rule which I cannot find as a standard rule anywhere (see page 2).

Thanks in advance.
The fact that a system is complete for proving valid formulas without the cut rule doesn't mean you can derive the cut rule from other rules. 

In fact it is not difficult to construct counter-examples. Consider 
$\Rightarrow A \rightarrow B$ and $\Rightarrow A$. From these assumptions it would follow that $\Rightarrow B$. But you cannot derive it without using a cut.