Can I ask a new employee's previous employer the reason of separation?

Oh, yes, you may certainly ask -- but don’t expect an answer. I estimate that 95 percent of all employers will only provide you with the dates of employment and title of past employees; and then they will confirm a salary level if authorized in writing by the employee to do that.

Savvy employers are aware that employees who lost out on job opportunities when a reference check revealed their poor performance or bad behavior, etc. will sue the past employer if they can for ruining their chances of gainful new employment. It does not matter if what the past employer said is true or not, as often "truth" can be conveyed in a variety of ways and -- is like beauty -- somewhat in the eyes of the beholder.

About the only way to obtain an honest assessment about a potential employee from a past employer is to know someone well enough that works at that company who is willing to talk with you on an assured confidential basis because they trust you.