If you use bash, then the terminal history is saved in a file called .bash_history. Delete it, and history will be gone.
However, for MySQL the better approach is not to enter the password in the command line. If you just specify the -p option, without a value, then you will be prompted for the password and it won't be logged.
Another option, if you don't want to enter your password every time, is to store it in a my.cnf file. Create a file named ~/.my.cnf with something like:
[client]
user = <username>
password = <password>
Make sure to change the file permissions so that only you can read the file.
Of course, this way your password is still saved in a plaintext file in your home directory, just like it was previously saved in .bash_history.