I am assuming you have two session/terminal of same Linux servers.
STEP 1:- Find out the terminal name. Type the below command on first terminal.
[root@lcoalhost ~]# tty
STEP 2:- Find out the terminal name. Type the below command on second terminal.
[root@localhost ~]# tty
STEP 3:- Find out the PID of terminal which you want to kill.
[root@localhost ~]# who -all | grep root
root + pts/0 2012-07-18 17:47 . 27981 (IP_Address)
root + pts/1 2012-07-18 17:47 . 27999 (IP_Address)
For example, you want to kill remote session /dev/pts/1 then just type the below command from first terminal.
[root@localhost ~]# kill -1 27999
Where 27999 is PID of /dev/pts/1 terminal.