I have in the past lifted the plant and divided it. it has a fleshy white tuber. not tried normal cuttings.
see what others suggest Ianplant.

Hi, the normal propagation methods for Alstroemeria is by seed, or division, sow the seed as soon as it's ripe in small pots, and keep in a cold frame, only put about 6 or 7 seeds in the pot, and plant out the seedlings by the pot full, as they don't like root disturbance, or divide established clumps in autumn, or very early spring, if you live in a frosty area, give them a mulch for the first 2 years, after that they should be fine without, Derek.