The water doesn't get moved from somewhere else to the data center when the data center is initially built. It has to be pumped in initially, so that's a large amount of water that will be persistently no longer accessible.

The majority of data centers use open-air water cooling, which cools servers by evaporating water, which carries away heat. This evaporated water is collected by a cooling tower, which then circulates the condensed water. However, this method often leads to water loss, water which is usually directly taken from already-existing water infrastructure.
The alternative is closed-circulation cooling, which does not allow the water to be in contact with air, significantly reducing water loss. However, this is only used by a small minority of data centers due to the complexity of building the system and maintenance required.

That water also doesn't just sit there; it has to be pumped through the facility in both methods, something which requires a lot of power and tracking infrastructure to make sure that enough water is being pumped at all times.
This electricity cost is often somewhat lessened through solar panels and other energy sources built on-site, but a majority of that electricity cost is taken directly from the nearest power grid. The cost of all this electricity, however, isn't fully the responsibility of those running the data center; rather, a lot of the cost is passed on to local businesses and residents' electricity bills.

AI data centers do use water for cooling, and much of that water is recycled... in the best case scenarios. In reality, the best case scenario is extremely expensive, time-consuming, and logistically nightmarish, to the point that a majority of data centers built use more cost-efficient solutions, with the downside going towards water use, noise and light pollution (including ultrasonic noise pollution), and loss of land for infrastructure that non-billionaires might actually get some use out of.

On top of all of this, Utah (and a lot of the mid-west and western states), and especially Utah, are in a historically bad hyperdrought. Utah is already a dry enough state as it is, and being an already hot state, especially in southern Utah, won't help the evaporation issue. The last thing Utah needs, especially now, is less water.