Unlike previous versions of the game, your wolf will not respawn if they die. The wilderness can be a harsh place! You can always start again or reload a previous save in order to try again.
Your mate cannot die. If your mate is stuck somewhere (like an 'invisible wall'), first try howling. If it isn't responding to you, just save and end the game, then reopen the affected save file. The issue should be fixed upon reloading. If it isn’t please submit a bug report and include the affected save file and as much detail as possible so the developers can investigate.
Pups can die
Just like in the real wolf world, pups are not invulnerable to dangers and threats and can indeed die. Starvation, predators, and drowning are all hazards you should attempt to avoid! They do not respawn (but you could reload an earlier saved game).