By shoving and pushing I don't mean shove it just to have it bounce back, but cracking and cutting down plants. I am not sure how to say this, let me just give you and example:
The airplane flew through the jungle and ___ the plants and foliage with its sonic boom, forming a permanent path through the jungle.
People also do this with a machete, like in the following example:
The guide ___ the thick foliage with a machete allowing the tourists to walk with more ease.
One "hacks" through the jungle, using a machete. This gives an impression of difficult movement, as is common in dense forests.
This works well for your second example. The first example seems odd to me, as a sonic boom is loud but doesn't cut down plants. Even if the plane flew low over the jungle it wouldn't create a path. If the plane actually crashed into the jungle it might leave a "trail of destruction". The situation is peculiar, but perhaps you could use "hacked" here too.
You can use the word scythe. The Oxford Dictionaries has:
scythe
VERB [with object]1 Cut with a scythe.
the first job was to scythe paths through the nettles
So your sentences could be
The airplane flew through the jungle and scythed the plants and foliage with its sonic boom, forming a permanent path through the jungle.
The guide scythed the thick foliage with a machete allowing the tourists to walk with more ease.
The scythe is a tool used in UK to do the job, we don't use the machete.
