As @Povilas S mentioned, the filtration system would take care of smaller organic waste (although you would likely still need a basic filtration system for collecting larger debris like leaves and twigs that fall into your pool, and also pumps to maintain pool circulation, which is also important in helping to keep it clean), but it would not address the other concern which is disinfection of microorganisms to prevent waterborne diseases and infections.
Wikipedia has a handy breakdown on what is involved in pool sanitation, in terms of various methods and the different sanitation concerns.
If you want to avoid harsh chemicals and also incorporate the clams and mussels for filtration you would need a hybrid approach to take care of the other concerns. Some of your best options would be:
In terms of how they work (detailed here):
"The water goes through the pool’s filtration system first, and then through the UV rays. The water flows through graphite housing where a UV light destroys bacteria, algae, viruses, and other microorganisms by attacking them through their cell walls.
Most pools with this system also use chlorine (just so the rest of the pool stays clean), but even then, they use much less than swimming pools that rely on chemicals alone. [...]
The UV light doesn’t leave the graphite chamber, which makes this a secure and safe way to clean your pool. In other words, you’re not going to be exposed to the light. Almost the entire process takes place within the system itself, and as an added bonus, it doesn’t need much maintenance."
In this case you would be replacing the chlorine with the mussels and clams for the general cleaning as well as the finer levels of the filtration and rely on the UV for killing the microorganisms, and a larger filtration system just for the twigs and leaves, etc.
The same way swimmers would be safe from the UV light it would also not harm the clams and mussels unless they were located in the same chamber.
B) Mineral sanitizers - This would help in avoiding harsh chemicals.
This link mentions these minerals in particular and their purposes:
"Silver and copper are well-known oligodynamic substances that are effective in destroying pathogens.
Silver has been shown to be effective against harmful bacteria, viruses, protozoa and fungi.
Copper is widely used as an algicide.
Alumina, derived from aluminates, filters detrimental materials at the molecular level and can be used to control the delivery rate of desirable metals such as copper. Working through the pool or spa filtration system, mineral sanitizers use combinations of these minerals to inhibit algae growth and eliminate contaminants."
Note: Don’t use salt pools if you want to avoid chlorine
It looks like traditional salt water pools would not be an ideal solution (despite clams and mussels being used to ocean salt water) as not only are the salt water generators expensive to install and maintainence a constant battle with corrosion they they also still contain chlorine as they are cholorine generators via electrolysis, though many people do not realise this and assume it is just salt due to the salty taste because they did not add the chlorine to the pool themselves. (Although they do have significantly less chlorine, for those considering a salt pool). Here is a useful breakdown of some pros and cons of salt pools for anyone curious about them.