If you could open one end of a portal on Earth at sea level, and the other in space, the Earth's atmosphere would vent into space, eventually leaving the Earth uninhabitable.  The larger the portal, the faster the process.  You could also steal away the Earth's oceans too.  Or, even mass from the mantle.  Steal enough mass from the mantle and the Earth's crust would have to do some dramatic shifting to compensate.