Every flight controller I'm aware of requires either a radio frequency connection to a RC controller, or GPS.
Both can be messed with. By building a drone myself, radio interference is a huge issue. A directed 1575mhz signal towards the drone would certainly interfere with its lock on the GPS satellites (my Ublox M8n gets disrupted just from other electronics on the vehicle!). And to knock out flight control, just emit something around 433 mhz, or 2.4ghz towards the craft and that should take it out. Granted emitting a powerful signal in those frequencies will have collateral effects, but with a drone endangering the white house, I'm sure that doesn't matter.