By small belt - do you mean the power steering belt? No, you do not have to cut it, you need to remove it to remove the alternator belt. Depending on its condition, it may also need to be replaces since you are there.
In order to remove the power steering belt, you have to loosen the screws holding the power steering pump (3 of them, 2x13mm, 1x14mm if I remember correctly), then loosen the length adjuster, then do the trick as described - observe which way the engine is turning, remove partially the belt from the pulley, crank the engine with ignition wire out of the coil just for a fraction of a second so that it comes off. Put it back on the same way, apply tension via adjuster, tighten the three bolts.