The left resistor sets the collector current (Iemitter+Ibase). The left transistor will sink the same current (minus Ibase). The right transistor will sink the programmed current regardless of the load resistance.
The left side is the program side. The collector current determines Vbe, which determines the collector current.
The current mirror works until the right transistor saturates (Vce < 0.2V). Other requirement is that the temperature of the two transistor should not differ.
