To determine the total cost of a spell, start with the mana cost or alternative cost you're paying, add any cost increases, then apply any cost reductions (such as that of Blasphemous Act). The mana value of the spell is determined only by its mana cost, no matter what the total cost to cast the spell was.

Blasphemous Act's ability can't reduce the total cost to cast the spell below {R}.

The total cost to cast Blasphemous Act is locked in before you pay that cost. For example, if there are three creatures on the battlefield, including one you can sacrifice to add {C}, the total cost of Blasphemous Act is {5}{R}. Then you can sacrifice the creature when you activate mana abilities just before paying the cost.

Although players may respond to Blasphemous Act once it's been cast, once it's announced, they can't respond before the cost is calculated and paid.