Is it safe to switch Vcc of Chip while IO still connected?
Probably not, unless specifically stated as such. One indication it isn't is a specification such as this one: 



When Vcc is 0V, it is not recommended to have more than 0V at the inputs. 

However, there are ways to isolate the chip you want to power down - for example using a voltage translator chip such as the 74LVC1T45 which is fully specified for leakage with one of the Vcc rails at 0V. 

As well, you should use a P-channel MOSFET to switch the power. Low = ON.