Firstly, you need to know selenium is a web automation tool. so it can only operate things belongs to browser. Even that, it can't operate all things belongs to browser, like address bar, favior bar, menu bar of browser.
For most case, the print dialog is not belongs to browser, it supplyed by OS or other software installed on OS. so selenium can't operate it is reasonable.
If your script code by java, you can use java.awt.robot to capture the dialog
and click 'print to file'.
If java.awt.robot can worked as your expect, I think you aslo need to set browser options in your script to give a path for browser to save the printed file, just like when you download file, browse will ask you where to save.
if you not to set that options, i guess it will pop-up another dialog to ask you where to save and this dialog is also not belongs to browser.
it's not easy to use java.awt.robot to set the save path.
Because you need to consider the possbility of script run on different OS, use abosulte path is not workable on different OS. Besides if your script run with seleniu grid, it will make you craze. So if testing print to file feature is not important, i recommend you test it manuall.