Basically what you're looking for is something like Pivot Tables of Excel, where you can group by anything you want.
Unfortunately there is no such support in Google Spreadsheet. What you (or someone) could do though is to write a simple script to group them for you. If you're interested you can start with some tutorials.
Using the Data->Pivot table report... offers exactly what you are asking for.
It might be possible that you have to use the "New Google Sheets".
I use that as a default setting and it was easy to achieve what you wanted, similar as in Excel.
Here in my answer I explain how to enable the new spreadsheets.
It seems I did not completly understand the problem.
First we need to have the month. For that add a new column to extract the date using =MONTH(DATE_COLUMN).
Best Answer
Just change the format by going to
Format
>Number
>More Formats
>More date and time formats
and choose or create the one that meets your needs.