You can't remove the acids, because they're dissolved in the liquid. You can, however, neutralise it.
Acid is basically $\ce{H+}$ ions dissolved in the water. By reacting it with a base, you do the following reaction:
$\ce{H+ + OH- -> H2O}$
So the acid reacts to form harmless water.
The problem is that you can't just add $\ce{OH-}$, you have to add it as some salt. Also, the citric and phosphoric acid you have in the cola were added are also dissociated from a salt or molecular form:
$\ce{H3PO4 -> H+ + H2PO4−}$ for phosphoric acid, for instance.
So whatever you put in there that reacts with the $\ce{H+}$ should also react with the $\ce{H2PO4−}$ ion to make something that's not soluble.
Usually, neutralising acids is done with carbonates such as sodium carbonate or calcium carbonate (also known as soda and lime, respectively). Both of which are safe materials to handle. The problem is that by doing that, you're introducing carbonate ($\ce{CO_3^2−}$) which might alter the taste.
A better solution is to add in hydroxides, such as sodium or calcium hydroxide ($\ce{NaOH}$ or $\ce{Ca(OH)2}$). The problem is that those are much more hazardous things which can easily hurt you if you don't use them properly. I would recommend using calcium hydroxide because then the calcium will react with the phosphate anion in the cola to make insoluble calcium phosphates and with citrate to make (somewhat) insoluble calcium citrate. Then you can just filter the stuff out and have your acid-free cola.
Basically, by adding in $\ce{Ca(OH)2}$ to your cola, you react the "acid" bit to make water, and you react the "phosphoric" and "citric" bit to make a white solid precipitate in the bottom of your glass.
DISCLAIMER
This is all in theory. I highly recommend against adding chemicals to your food and drink. If you don't like the acidic taste of cola, don't drink it. Find another brand or another drink that you do like. Tea? Anyway, do not mess with your food unless you know exactly what you're doing and you know that your chemicals are food-grade and safe. Don't go and do stuff with your cola just because someone on the internet (me) told you it will work.