The Greek reads washing (G3067 λουτρόν loutron) of regeneration (G3824 παλιγγενεσία paliggenesia), not mikveh. They are two completely unrelated processes. Regeneration is spiritual. A mikveh is physical and mystical.
Many commentators understand "washing of regeneration" to mean water baptism. Washing = water ... regeneration = rebirth. So The use of mikveh here is a paraphrase used to convey the meaning to a Jewish audience in a way they would immediately understand.
David K Bernard explains it like this:
"Titus 3:5 is a companion verse to John 3:5, and it apparently refers to water baptism. "Not by works of righteousness which we have done, but according to his mercy he saved us, by the washing of regeneration, and renewing of the Holy Ghost." Regeneration simply means new birth, so here is a second passage linking water and Spirit with the new birth. The wording of this verse points strongly to water baptism rather than to the other alternatives. It describes a specific act of washing, distinct from the work of the Spirit.
Many translations emphasize the connotation of a specific act: "the laver of regeneration" (Conybeare), "the bathing of the new birth" (Rotherham), "the bath of regeneration" (Weymouth), and "the water of rebirth" (New English Bible). This act of washing is a cleansing from sin, which brings to mind Ananias' instructions to Paul: "Arise, and be baptized, and wash away thy sins, calling on the name of the Lord" (Acts 22:16). Paul recounted the story in Acts 22 and wrote the words in Titus 3, 50 presumably he was aware of the parallel thought.
The conclusion is inescapable: "the washing of regeneration," which means "the new birth of water," is the washing away of sins at water baptism. Indeed, according to Bloesch, "Biblical scholars generally agree that the washing of regeneration refers to the rite of baptism." [34]