When TDS on GST is deducted @2% do we need to deducted TDS under income tax act also

We are a school (registered and Societies Registration Act, 1860 ).  we are not registered under GST Act as educational institution are exempt.   now we are building new classrooms ,playground through a contractor with proper contract agreement..... now the bill he is issuing is always more than 2.5 lakhs excluding GST.  

so, my query is  do we need to deduct TDS on GST (section 51)  if yes, then will we have to register under GST act. 

Also if we deduct TDS under GST act then TDS under Income tax act also has to be deducted   that means we will have to deduct 3%   (1% to be deposited to income tax deptt & 2% to GST deptt./)

Please clarify