Can my CC company stop specific purchases?

• accept credit card payments online
• apply for credit card online
• accept debit cards online
• xbox live help
• xbox live helpline

So I caught my 14 year old son using my debit card for his Xbox account he racked up a bit of money I have not disputed yet but will soon but before I do I want to know, if I can just block Xbox Live purchases and not block all online purchases because I do quite a bit of purchasing online myself but there is usually just an option to block online purchases. Once I dispute will they automatically block all Xbox Live purchases?

Can my CC company stop specific purchases?