The easiest way to get past most of the vines blocking doors is to use the Combat Radial menu, then change target mode so that you are targeting objects instead of enemies or friends. Once that's done, you can use the shoulder bumpers to change between objects and shoot the vines on the door.
If you are using a melee character to do this and they aren't close enough to the vines, then the attack might fail, so you might need to move closer. It's also possible to throw explosives such as TNT to get past.
Note: There are also larger vine clusters in Ag Center which can only be destroyed after you release the Ag Center infection cure into the ventilation system. Those larger vines can't be destroyed by attacking them.