I'll tear his eyes out and suck his fuckin' skull

[MW]

meaning?

[Tdol]

I intend to do him some harm.

[rewboss]

"Fucking" is an expletive -- "bad language", as a mother might say to her child -- and one you should not use in polite company. In fact, if you're not a native speaker, you shouldn't use the word at all unless you are really, really certain it's OK. In fact, it's bad enough that you'll often see it printed as "f---ing" in some newspapers and periodicals.

We're left with a very violent and graphic metaphor. It's not an idiom as far as I know, except perhaps among certain groups of people, but it is clearly a metaphor. If it were possible to actually do it, it would be a very unpleasant and messy way to kill somebody.

A much less offensive threat would simply be: "I'll kill him!" A more colourful metaphor is "I'll have his guts for garters"; it's actually no less horrible (it means, "I will use his intestines to hold up my socks or stockings") but has been used so often, it's now OK to use it in polite company. (As long as you don't also add "the F-word".)

[MW]

This comes from the movie Wall Street

I think it mean to do violence to someone who did something really bad to you

[Tdol]

It might be a slight case of hyperbole.

[curmudgeon]

It might be more accurate to say suck his brains out (but no less disgusting)

[Hanabi]

Maybe you shouldn't know...

However, it would be rude and mean to say, cruel.

Tear is to pull out, eyes are, well I'm sure you know what eyes are.
To suck it also to pull out, and skull is a skull.
"Fuckin'" is a form of "fucking" and in this tense is, advern, adjective? Whoever said this put that in to express his anger or hate.

* I'm not going to explain the two nouns eyes and skull
** Tear can mean to rip, but in this tense I'd say it means to pull
*** Fuck, the simple form, is a simple slang word, has many forms and can be pretty much every part of speech, not a nice word however, "swear word"

(I'm not good at explaining things now am I?)