There is only one herbicide that does not kill the St Augustine itself. That is atrazine. Atrazine is fairly dangerous, so read the label very carefully. For example, it will tell you to walk backwards when you spray it. Don't walk through the sprayed area.

When you spray you might not see the results you expect for a week or so. Then suddenly you'll notice that all the weeds are gone.

Oh and I believe that is spurge. Is it milky when you break the stems?

No, it is not milky when you break the stems.

I used some Atrizine on this, and it did not kill it.

"Metsulfuron has also been shown to be an effective weed killer in St. Augustine grass. Care must be taken when using metsulfuron on St. Augustine lawns that have been mixed with Bahia grass because the herbicide will kill all the Bahia grass."
Reference:
http://www.gardenguides.com/131562-weed-killer-st-augustine-lawns.html

My dad used metsulfuron on his St aug lawn, killed all the weeds and the grass looks great. This stuff is much cheaper than atrizine and is much more environmentally friendly.