I would translate "way" with mores.
It is not "way" in the sense of a path but in the sense of traditional ways.
I interpret that you want to say, roughly, that the world has given up its traditions.
My suggestion for a losing verb in this context is perdere.
Your choice amittere means throwing away, which is also possible if the world has lost its way willfully.
If you want something easily understood by someone who knows English, perhaps the best choice is omittere, meaning things like "let go, neglect, dismiss, disregard, omit".
Mundus is a good choice for the world.
You can always use the suum if you want, but it can also be understood implicitly.
In this case there is little room for ambiguity, so I would consider it somewhat more idiomatic to leave the reflexive possessive pronoun out.
So how about mundus mores omittit?
Or if you want to fit it into hexameter with a similar Roman sentiment: Tempora mutantur, sibi mores mundus omittit.
Or with a slight variation, closer to the original: Tempora mutantur mores et mundus omittit.
Postponing et by ine word from the expected position is a feature of the original verse too.