Nah, it cuts like soft stainless-steel. Garden-variety bolt-cutters will go through it like butter.
To wax poetic for a little while, Ti is lightweight, strong, warms quickly to the touch but isn't cold in winter, resists abrasion, doesn't irritate, and is almost immune to corrosion. Its strength allows a lower-profile ring without collapse, too. When making rings for our wedding, I could have used any material under the sun; titanium was our choice.
A material need not be rare to have significance, so it is with love.
It's a real hazard that is well known in the trades, but might not be appreciated by people who are attracted to the idea of an exotic metal ring but are not in situations where they will be warned about it. The warnings here seem reasonable to me.
There's an easy workaround -- if you're working in a machine shop or where getting your ring caught by something is a possibility, the ring goes in a safe place.
For me, before I touch a lathe or mill, the ring goes in my left back pocket. Every time.
The ones I saw from a quick search were nice looking but pretty pricey. Basic Gold rings were going for the same price as some of the fancier designs so I think that would be more of a design / aesthetic choice.
Titanium / Tungsten / Silver are for people who want an inexpensive ring.
Funny because titanium is actually a very cheap material. I got a 1" cube of it for about $30. I assume almost all of the price is labor for working with it rather than the cost of the metal itself.