Can we terminate an employee on performance grounds if he doesn't wish to resign from the services?

Dear Professionals,
I have the following queries :-
1. Can we terminate an employee on performance grounds if he doesn't wish to resign from the services of the company even after being counseled on his performance issues?
2. What should the letter state if we have to terminate him on performance grounds, considering that he is not resigning even after being told to do so ? (sample letter templates shall be helpful)
3. In general, how can this issue be dealt with smartly with both the parties being separated with mutual understanding and healthy way?
4. Does termination on performance grounds stands a justifiable reason in the court of law if the issue takes a legal turn from the employee's side?
Awaiting your valuable responses.
Regards
Jigar

Mr. Name
Emp id - id
Dear Mr. <name>
This is with reference to the letter issued to you for joining our training batch of <date>
On evaluation of your performance during the training period we found that you have not shown adequate progress and have scored less than the expected marks in the assessment tests.
The company as per the clause given in your letter reserves its right to cancel your selection as a <DESIGNATION>
We regret to inform you that we do not require your services with effect from <date>
Wishing you good luck in your future endeavours!
Yours sincerely,
HR MANAGER

Hi
Sample letter of Termination of employee on Performance grounds
Mr. Ravishankar V.
C-13, Bhatia Gardens
Manapakkam
Chennai-600116
Dear Mr. <name>
This is with reference to the letter dated <date> issued to you regarding extension of your probation period for a further period of three months with effect from <date> to <date>
On evaluation of your performance during the probation period and thereafter, we found that you have not shown adequate progress and have not made any significant improvement in your performance inspite of repeated warnings.
Based on the above observation, we regret to inform you that we do not require your services with effect from <date>
As per the norms of the company, we give you one month's notice from the date of this letter.
Yours sincerely,
HR MANAGER
Thanks
Sambala