I hired a contractor in Sep.8/14 to have my kitchen renovated.

These cases are certainly not uncommon. A contractor commences work, does a negligent or otherwise deficient job, so the customer refuses to continue paying, then the contractor walks off the job. Generally, the contractor will refuse to return until s/he receives further payment, so the only way the customer can get the job completed is to hire another contractor to fix the improper work (of the first contractor) and also to complete the outstanding work.
So, the way these cases are generally dealt with is that the customer sues the contractor (often in Small Claims Court, assuming the amount is within their jurisdiction) for (i) amounts paid for services never performed, (ii) amounts paid to other contractors to fix the first contractor's sloppy work, and/or (iii) amounts paid to other contractors to complete the job that the first contractor never finished despite being paid to do so.
Sometimes, the contractor will come around and counter-sue the customer for money the contractor feels s/he is still owed.
As such, it will come down to who can prove their case. If you intend on suing, it is best to start gathering evidence immediately. Photos of the state in which the contractor left the project are generally very useful, as are any invoices from other contractors you paid to fix the first contractor's sloppy work. It may also be wise to keep a diary of any and all problems you experience with the contractor, e.g. all the times you asked him to do Task X but instead he decided to work on Task Y and never completed Task X.
In summary, yes you can sue the contractor but it would be prudent to gather as much evidence as possible in the interim.