In your team you have an under performing team member who is affecting the performance of the team?senior management is rejecting your decision to

The first approach is to really try and understand the reasons for the low performance and bad influence.

If as described, you cannot repair it yourself, that team member needs to be isolated.

It is a strong punishment to keep that person isolated from the team, to take away from him/her the social status of being part of the team and understanding the progress and the common language between the other team members.

The management can decide not to give you a replacement, but you as a team leader can decide not to include that person in the team assignments. I believe this person would try all his/her effort to BELONG again.

if it is YOUR team (as the question says), YOU should have a say about the team composition. 

If it is YOUR team, then YOU are "on top of what goes on" in the team, and no one (I mean it) should be forcing you to accept someone if you do NOT approve having him in YOUR team 

If it is YOUR TEAM, and you are "accountable" for the results, then you should also have the "ownership" and "empowerment" to run the team to produce the desired results 

If things are out of order, it is up to you to decide whether to accept to continue in the situation you just described, or tell top management (fair and square) to start searching for another team leader , or to "waive" the responsibility and liability from your shoulders to their (top management) shoulders 

Finally, if the situation is like what you described, and you can prove it with facts and numbers, I find it very strange why top management would not listen to you !! 

Thier is a basic diffence between organisation and individual behavour both affect the bottom line performance of groups. Is it emmotional issues that is colliding with work demands.Is it too much stress.Is the renumeration not meeting up with his personal domestics demands.what are his real area of competence in the the last couple of monthe since joining the organisation.Is his speciality really functioning in the team. Better and effective councilling is the start of the solutions.

There is what we  call employee resistance for training process & this relates to many factors & reasons  (age of the employee- employee intelligence- employee skills & knowledge- culture- employee attitude   ...etc . So one of  the Premises polices & procedures is the evaluation process & employee performance score report .If the employee still in probation period & his performance is not up to standard you can fire him or transfer him to such department meets his capabilities & qualifications. if the employee passed the probation period & no way to improve himself  or his skills there are many options for that :-

1- You can re qualify him .

2-You can transfer him to other department if available. 

3- If he is in  the position of first line staff & he is a guest contact  & you are  afraid  about the

     premises  reputation  & no other choice from firing him & ending his contract do it  n a very

    peaceful way .

4- Go back to your motivation policy & procedure & try to motivate him

5- Finally revise your recruitment policy & procedure may be something  wrong in interview &  

     hiring  policy  or  the interview committee is not efficient enough in interview process.