They sell blower motor resistors also. Not that...it helps you with your task. Just that it might be an option. 
Is this for a RHD or LHD Mini, it looks very much like the guidance for a LHD ??Working under the drivers side dash toward the center of the console. simply remove the side panel. You may have to use a torque's screw driver and remove the lower dash panel first!
After you have removed the panel on the center console. It is simply a matter of removing the blower fan by disconnecting the harness and removing the bolts.
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Installation is in reverse.
Now working forward and above the accelerator pedal at the side of the heater(center console.
Unclip blower resistor retaining clip (A) and pull out of housing (ARROW).
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Detach electrical connector and remove sensor.
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installation in reverse.
Working above and forward of the accelerator pedal at the side of the heater A/C housing(center console)
Detach electrical connector (ARROW)
Rotate final stage counterclockwise slightly to remove (CURVED ARROW)
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When installing, make sure markings on final stage and housing line up.
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button everything up and your good to go!
They are a doddle, looks like you have to take the whole dash out to do a RHD oneIt's an LHD.