I think you need to understand power supply specs.
When it is said that a power supply is 3.3v and 30mA current, it usually means that the voltage is fixed at 3.3v, and it can supply any current upto 30mA.
Meaning that if you take more than 30mA current, then there is no guarantee that the voltage will remain at 3.3v, and usually the voltage will drop down.
This is a constant-voltage power source.
On the other hand there is the constant current source. Your Current mirror bjt circuit is a simplistic example. Here, the current remains constant at 30mA, but the voltage on your collector will vary depending on the load, and a high enough resistance will saturate upto the main supply voltage, at which point the current will start decreasing.
Now if you want to have constant voltage AND constant current at the same time, then all you need is a fixed resistor load !!!
In your case, 3.3 v and 110ohm will be exact 30mA. But thats pretty useless.
So now you need to clarify your thoughts, and explain what you really want to do?