Grammatisch gehen alle drei, aber ich habe keine Ahnung, was du sagen willst.

Gemeint ist mit dem Spruch, daß sich jemand, der mit mittlerweile ungeeignet gewordenen Mitteln seine Arbeit viel zu langsam erledigt, meint, sich nicht die Zeit nehmen zu können, seine Mittel in Ordnung zu bringen, um danach damit wieder effektiv arbeiten zu können . . .

I don't have time to sharpen the axe, ...
I haven't got time to sharpen the axe, ...
I've got no time to sharpen the axe, ...
... I've got to chop wood.
... I have to chop wood.
... I need to chop wood.
... I need to be chopping wood. (= right now)
... I've got to be chopping wood.
... I have to be chopping wood.

All those sound equally okay to me, though in AE at least, 'don't have' is the most common. In more formal writing, you would need a semicolon instead of a comma, because there are two independent clauses, but that would be unusual in the written version of a spoken sentence like this one.

The only things that sound odd to me are 'the time,' which usually means the time of day, as in, Excuse me, do you have the time?, and 'as,' which is much more formal, as if in German you were to say '... denn ich muss Holz hacken.'

If you use 'as,' however (which I don't recommend), you must put a comma before it.

Danke Daddy für die treffende Erklärung :-)

Und an hm -- us: Vielen Dank für die ausführliche Antwort! Ich persönlich mag "haven't got time" am liebsten. Sofern mir also keiner schreibt, dass das in BE zu komisch klingt, werd ich also "I haven't got time to sharpen the axe, I need to chop wood " verwenden (um ein doppeltes "have" und "got" zu vermeiden).

Schließe mich dem Dank an Daddy an. Ich verstehe es jetzt.

>>um ein doppeltes "have" und "got" zu vermeiden

In English, that is absolutely not an issue in a casual sentence like this with short familiar words.

What you don't want to do is to repeat a word that will catch your attention several times in the same sentence or paragraph. But here, the content words are 'sharpen the axe' and 'chop wood'; the rest is just background.

...und für wen es interessiert:
"Give me six hours to chop down a tree and I will spend the first four sharpening the axe." -- Abraham Lincoln

Es gibt unterschiedliche Versionen dieses Zitats (cherry tree, eight hours usw.), aber dem Inhalt nach scheint es authentisch zu sein.

Sounds like a couple of departments I could mention. They never have the time to do sth properly, but they've always got the time to do it twice. *fg*