Laying off for poor performance is not a right practice. Initial screening, then preliminary & final interviews, group discussions (if applicable) etc are various processes involved in selecting a right talent for an organization. However, a newly hired candidate, after putting his services for a few weeks or 2-3 months, can perform well or vice-versa. This is because of "Expectations v/s Realities"
of a new candidate in that organization.
There are various factors/driving forces in any organization which can either motivate or demotivate an employee (particularly a newly hired employee) which will ultimately lead to good job performance/poor job performance.
Kindly examine these factors and openly discuss and counsel the employee concerned.
Also introduce and implement a Performance Improvement Plan.