Well you should wait until it is either drained of power, or pull the battery, before taking out the SD Card. You should be able to read it on any device that can use a SD card, as long as the card had not been changed to "Internal" storage rather than the standard "External" storage. If it had been, then it would be encoded and only viewable by that device.
Another way would be to try (while the device still has power) to connect it, via USB cord to a computer and see if it you can access the SD card as a folder that way. If you can, you would then be able to move the files over to a folder on the computer. Also, if you can access it that way, you should also be able to access the files on the device itself the same way.
Now if you can't access it through connecting it to a computer (some devices just won't if you can't touch the screen prompts) then I know of no way to get the data off the device itself, without fixing the screen.