Everything that lives will ultimately die.  In the case of the algae culture, the death usually ends up as a layer of dead cells at the bottom of the culture vessel.  These cells will begin to decompose pretty rapidly through bacterial and fungal action.   Bacteria and fungus will consume oxygen and release CO2, which is the opposite of the process of photosynthesis.  In many cases it is ok, even good, to have decomposition (sometimes called remineralization) taking place in your culture vessel.  This is the case in aquariums with biological treatment of wastes.  As was said in the Lion King, it is the "circle of life".  

However, if you are trying to grow a mono-culture of algae, the detritus can introduce growing conditions that are outside of ideal for your goal- so you must remove the detritus.  Three ways to do that are discussed below:   Filtration, suction, and decanting.

Filtration:  As cells decompose they will clump together into amorphous blobs.  It is a goal of the bacteria and fungus to have dead cells stick to the other dead cells.  In doing so, the size of the 'floc' is often larger than the size of the individual microalgae.  This size differential can be taken advantage of by filtration with a screen that is ~5x your cell diameter.  So if you are 5uM, then a 25uM screen will work well.  You can pour the culture through the screen or have a pump constantly filter the culture. 

Suction:  Here simply use a siphon or pipette and target the detritus at the bottom of the culture vessel.   Target the material on the bottom and dispose of what you collect.

Decanting:  If you have ever had a good German beer, you will often see yeast at the bottom of the bottle.  The label says to 'decant before serving'  meaning, pour the beer into a separate glass without pouring out the yeast on the bottom.  This is exactly the same action you should consider in decanting a culture.  Pour the culture from one container to another clean one.  Dispose of the waste at the bottom of the first culture.