I understand that one of the meaning of the word ' marry' is " to give in marriage ".
Hence is the following sentence correct or not- grammatically?
" As I am marrying my daughter please grant me a week's leave."
In the example you've given, the person asking for leave would be more likely to say something like 'May I take a week's leave for my daughter's wedding or 'My daughter's getting married. May I take a week off?'