There is nothing saying you shouldn't have a print button on your mobile website, but it is not necessary. The browser the user is visiting your site from has every capability to provide the print functionality the user is looking for. If the user does not see the need to print from their mobile device, they aren't going to care about having that capability. If they do care about having the ability to print an article, they will use a browser that supports such functionality.
Printing from a mobile device is not a straight forward task. Here is one article (of many) about how to Print from Your iPhone, and another about Everything You Need to Know About Printing From your Android Phone or Tablet.
If your user has the ability to print from their device they have gone through a series of very purposeful steps to allow them to do so. They will already be very familiar with what browsers allow them to print in the manner they are wanting. Don't try to second guess them.
So, while a print button might save the printer-savvy mobile user a little bit of time it isn't going to benefit them since they will already know where the print button is.