R Aryeh Kaplan in his beautiful book Waters of Eden (also part of his Anthology vol. 2) writes this is a chok and cites Bamidbar Rabbah 19:8
By your lives, a dead person doesn't make things impure, and the
water doesn't make things pure. Rather, God said: I have engraved a
rule, I have decreed a decree (chukah chakakti, gezeira gazarti), and
you have no permission to transgress what I decreed, as it says "This
is a chok (rule) of the Torah."
He then goes on to provide some explanations, knowing full well they are only an incomplete picture and the full rationale is beyond the human intellect.
- Water is a cleansing agent. The same way we wash with water, we also purify with water
- He describes at length how a mikve is like a womb and how one emerges "anew" from the mikve. Like a womb is full of water, so a mikve
- By placing himself in the water of the mikve, a person enters a place where he cannot breathe, therefore cannot live. When emerging from water, he is like born again (incidentally, he writes this is one of the reasons a mikve as to be directly in the ground, like a grave)
- He describes water as the ultimate fluid, the substance that most represents change and unstability (see Bereshit 49:4), while earth is stability and permanence. Until God brought water in the world, no life or change was possible. Water is life, earth is death (and thus we return to earth after death). When immersing in a mikve, one spiritually immerses in the basic concept of change itself, nullifies one's ego (which represents our permanence) and emerges renewed and re-birthed. Water represents change, and therefore that no evil is ineradicable, and no sin unforgivable ("repentance can wash away any sin"). Water therefore represents spiritual cleansing
- He has a long section on the analogy between mikve and the water of the river from Eden (i.e., water as the primary connection to Gan Eden) - too long to summarize here - see original if you are interested
The above summary is a very inadequate representation of R Aryeh Kaplan's beautiful words - you should read the original for yourself.