It's not difficult for an army with sufficient siege capabilities to block or destroy a portion of an aqueduct, thereby restricting and depriving a besieged city of its water supply. It was indeed a standard preliminary offensive measure from a belligerent army in initiating a siege.

In the case of Rome, this happened during the Gothic Wars wherein particular during the siege of 537-8, the Gothic army cut the aqueducts that crippled the city's supply capacities. However, the Goths were not able to fully utilize the deprivation of Rome's aqueduct to their advantage because they were unable to establish a full blockade of the city. Supply shipments from Byzantine controlled Ostia were still able to reach the city and Rome was able to hold out until reinforcements allowed the Byzantines to breakout and rout the besieging Goths.

In the case of Constantinople, we are given the demonstration of countermeasures a city could establish to the cutting of their water supply. In the siege of 626 by the Avars and Sassanids, the Avars destroyed the Aqueduct of Valens but to little effect because neither they or the Sassanids were first unable to achieve a naval blockade on the city thus allowing the Byzantine fleet to protect supply shipments from overseas. Secondly and more importantly, Constantinople boasted massive cisterns that were designed for the particular purpose of maintaining a water supply during a siege. These cisterns allowed Constantinople to essentially be independent of external water demands in times of siege although Constantinople was very much an exception in both the remarkable size and effectiveness of its cisterns and it's ability to withstand the supply deprivations derived from prolonged siege.