Can I use 1 mm² wire for 24 VDC / 15 A load?
My answer would be no because the voltage drop will be 0.77V (not 0.5V) and at 15A, it's 11.5W you are losing heating your wire.
Even if it may not heat too much, and you won't risk a fire or burning yourself (yet be very careful), it's still a lot of energy wasted. Even with 2.5, you still lose 4.7W.
Therefore I would recommand a 4mm wire to be within acceptable range. 

Working with low voltage and high current, you must always choose the thickest wires as possible. You can also use two or more wires in parallel if the gauge of a single wire is too large. If there is only one small screw terminal allowing only one small gauge wire, you can also connect a very short wire to a bus terminal for larger gauge wires and connect one or several larger wires for the longer distance. Yet, it would make no sens to build a power supply without enough big terminal for the current it's able to provide. Often they offer two screw terminals on which you can attach up to 4 x 2.5mm wire (one on each side of each screw).
Always use single strand (monolithic) wire.

Addendum: For short duration, less than one minute with several minutes in between when it can cool down, a smaller gauge may be acceptable. But you must make sure there is no risk of the motor running longer and that you or somebody aware of that are the only persons operating the device.