The answer to this, I recon, *is that they don't*.

They use molecular oxygen (O<sub>2</sub>) dissolved in the water for respiration, where is acts as a terminal electron acceptor, just as we use molecular oxygen in the air for respiration. We can speak of the water as being *oxygenated*. 

What *is* split in photosynthesis, where **reducing equivalents from water** are used to reduce NADP<sup>+</sup> (giving NADPH).

One of the great discoveries of biology, IMO, **is that the oxygen formed in green-plant photosynthesis comes from water, not CO<sub>2</sub>**.


Despite claims to the contrary, most infamously by Racker (1976, pp 28 - 29), but also by (for example) Madeira (1988), water is *not* split in the tricarboxylic acid cycle (Krebs Cycle). That is, reducing equivalents from water are *not* passed down the respiratory chain, or in any way used to make ATP, or are in any way a 'source' of free energy.  Such claims, IMO, are nonsense.

Great question, BTW.

**References**

 - Racker, E. (1976) A New Look at Mechanisms in Bioenergetics.  Academic Press, New York.  
 - Madeira, V.M.C. (1988) Stoichiometry of Reducing Equivalents and Splitting
of Water in the Citric Acid Cycle.  *Biochemical Education* **16**, 94 - 96 [pdf](http://onlinelibrary.wiley.com/doi/10.1016/0307-4412%2888%2990069-6/pdf)