Does it mean once the block is mined with transactions, the same block cannot be mined to add new transactions to it ?
Thanks.
Nope. The set of transaction is hashed and included as merkle root. The merkle root is included in the block header which is hashed again. If you add transactions, the merkle root will be changed and the whole block header will be changed. You can do it, but the block won't meet the target anymore and nodes won't accept it.