It may be possible but difficult for individual . Many stipulations (conditions) are done so that no one will be able to do so.
1) Taking over the down link: One can take over the information sent by a satellite and use its data, but the satellite sends the signal back to earth only when its allocated ground station is visible. If someone sets the ground-station very near to it, then also the person will require to know many satellite information like, exact frequency, type of modulation, method of encryption etc. which is known only to the actual ground station people and not disclosed publicly.
2) Taking over the up-link: This is major issue and is point of concern for all space agency. If some unwanted people gets to upload unwanted data, they can change complete working of satellite and they can configure the satellite in the way they want or can spoil the satellite. To prevent this every satellite is given a unique id, the up-link data is encrypted and certain protocols are followed. Again to up-link some data the person should know the frequency and modulation scheme.
With these provisions mostly all the satellites are saved from hostile attackers.
