It appears that machining titanium at cryogenic temperatures extends tool life:

Cryogenic titanium machining improves cutting-tool life by a factor of 10 with appropriate material removal processing speed. The Joint Program Office in coordination with the F-35 Fracture Control Board (FCB) approved the new process for standard roughing operations, impacting the most time-consuming and cost-intensive machining processes associated with manufacturing titanium parts. Broadly applied, this new technology could improve affordability and efficiency in the production of the F-35, which is approximately 25 percent titanium by weight.

My guess would that this generates smaller chips, that it might prevent material from adhering (galling, welding, etc.) to the tools, and it might slow the formation of an oxide coating, but I’d love to hear the theory behind it.

I would make an observation here:  If you have an aircraft that is 25% by weight titanium, you have a very expensive aircraft.