The network, a private entity, can shitcan anyone for any reason, including speech.
The Constitutional protections for Speech do not apply to private entities.
Where it gets dicey is when / if they do it at the BEHEST of the gov't. Then they are effectively an agent or arm of the gov't, and THEN Constitutional protections apply.
His joke wasn't that bad (or good), and I don't see it as any more of a call for violence against the President than Sarah Palin's "crosshairs" on a political map as a "call to violence."
People read too much into shit. A form of confirmation bias. Both sides do it, and I normally HAAAAATE when people say "both sides," especially when it's not true.