I sent a message to Max Gladstone via Reddit, and he replied:
Hah, good question. The title springs from a Bertrand Russell quote, which I first stumbled upon out of context, but which is from his book Marriage and Morals: To fear love is to fear life, and those who fear life are already three parts dead.
It struck me as appropriate for thematic reasons, which might take more time than I now have to elaborate on
But "three parts dead" means "three out of four parts dead" e.g. almost entirely dead.
Which tickles me because Kos is not as dead as he first appears
Thematically the short version is that the murder and reconciliation plot is driven by a fear of love, of a mystical sort--Gerhardt's fear of Kos and Seril's love, his inability to trust Kos, etc. And Tara is, on some level, suspicious of the surrender of self involved in worship...
Anyway! It seemed apposite.
As a small addendum, before getting Max's answer, I expected the "three" part to be possible arbitrary because the theme of the naming of the first six books is that the number indicates where the book lies in the series chronology. The order of events in-universe is Last First Snow, Two Serpents Rise, Three Parts Dead, Four Roads Cross, then Full Fathom Five. Ruin of Angels basically starts a new series in the world, so the author didn't use the numeric titling setup.
Oh, and as for the numbering—the number in the title indicates where the books fall on the timeline. 2SR is set a couple years before 3PD; FF5 is set a few years after 3PD, and [the next book] is set a big before 2SR. It all makes sense!