Microsoft has released an update that will fix the issue if your Skype crashes in Windows 8.1.

When you start the Skype Windows Store app in Windows 8.1 or in Windows Server 2012 R2, the app immediately crashes, and Windows returns to the Start screen. This issue occurs when the computer uses an Intel(R) HD Graphics 3000 (Sandy Bridge) graphics device.

Visit KB2902892 for details.