to wipe a surface clean, and from that, to blot out: to erase a record, a name, or a person until nothing is left.
The plain action is wiping. A hand wipes a mouth, a cloth wipes a dish, water washes ink off a page until the writing is gone. Every other use of this word grows out of that one gesture, and keeping the picture in mind is the key to all of them.
From wiping comes erasing. To wipe someone's name off a record is to blot them out, to make it as though they never were. Israel pictured a heavenly ledger, a book of the living, and this is the word for striking a name out of it. The same idea covers wiping out a people or a city entirely, leaving no remembrance behind, which is why it can describe destruction as total as the flood undoing the world God had made.
Its highest use turns the gesture toward mercy. When God blots out sins, he wipes the charge off the record so completely that it is gone, like a cloud burned off by the sun. And at the very end the same hand that could erase a world instead wipes the tears from every face. One verb carries all of it, because in each case something written or present is rubbed away until it is no more.
The range is wide but the center holds: to make something cease to be by wiping it out, whether that something is dirt, a name, a nation, a sin, or grief.