There are two known ways that Arcane Rot can reproduce.
The first method is asexually, where the rot simply spreads on its own where there is an ample source of magic. One can split a rot "eye" in half to trigger this process manually.
The second method is through the "Bloom", a rare event where the Arcane Rot will retain all of it's magic until it can reach the surface and spread billions of spores in the air, reaching large distances to find other Arcane Rot to exchange genetic material. This is how the The Rot Tower was created in Yew Nork City.