It would be a lot easier to reply to you with specific suggestions if you gave more information, such as work location, home location, whether your wife will also be working, etc.
Here are a few suggestions on how to cut down on costs. I think that some you probably already know because they're quite general.
1. Food
Cut down your food costs. You could probably live on HKD 6-7k/month if you eat simple food at home or cheap food outside. Find the best prices for your food.
2. Transport
Get your employer to get a place near your work location and within walking distance of an mtr station and bus stops. Send your kid to a kindergarten nearby. You'll save a lot on tranportation costs. I can't say how much you'll need because you didn't give much information. Make sure you live in an easily accessible place, so that you won't need to take taxis.
3. Child's Education
Consider how much you want to spend on your kid's education. A kindergarten can range from HKD 2-6k/month. Find your money's worth. Consider whether you want to send your child to extra activities or whether you can do those things yourself or form playgroups within your neighbourhood. Consider whether you would like to buy new books or borrow books from the library or buy secondhand books. If you are afraid of them being dirty, you could clean them again yourself.
4. Utilities
If you have to pay for your own utilities, use the regular methods to save electricity. Appliances that don't guzzle up energy, only turning on the AC when needed, closing the fridge door quickly,etc.
5. Domestic Help
Don't get a domestic helper. Hiring a foreign domestic helper would set you back HKD 3,580/month + airfares, health check-ups and other costs. I do not recommend illegally paying below the minimum wage for foreign domestic helpers.
6. Tax
Since you are working in HK, you need to check whether you will be required to pay taxes.
7. MPF
If you will work here for more than 13 months and are not covered by an overseas retirement scheme, you will need to contribute to your own Mandatory Provident Fund.
8. Other Expenses
There are obviously a number of other expenses, such as clothing, airfares, family outings and other unexpected costs. I highly recommend saving a substantial amount per month for such extra and unexpected costs.
It might be easier for your family if your wife works as well. She doesn't need to work full-time, if you are working about your child's upbringing. There are also some jobs that can be done at home.