Why does the Pressure ratio across the compressor increases when the mass flow rate is reduced?
The simplest way to understand this is to refer to Bernoulli's Theorem.  When the flow of a compressible fluid (in this case air) speeds up, the density of the compressible fluid goes down (and vice versa).  Pressure is directly related to density, so pressure also goes down when flow rate (velocity) goes up.  

Mathematically, Bernoulli's Theorem is expressed $\rho \times v =$ constant.  

Here, $\rho$ is density, $v$ is velocity.  

Look at a diagram of a Venturi tube, and it will make sense.