For the first time in my life I tasted smoked beef. It tasted mostly like ash. It didn't have any raw taste but just wondering when meat is smoked, does it get cooked thoroughly?
If the smoked beef you tried tasted of ash then it was not done right.
If done correctly and cooked to a safe internal temperature then, "YES" it is 100% cooked.
You should note that it is the internal temperature and not just "smoking" that is the rule for "doneness". Smoking can occur at a lower temperature. Smoking can be used to "cure" or preserve beef, as @TFD & @Aaronut point out. These process yield a product that is 'ready to eat' so I would say it is "100% cooked".