What is the meaning of the phrase "To cut along"?

[Issidora]

Business Idiom in English, Intermediate level

ESL/EFL Test #130 "Way of saying goodbye", question 2

If you don't ........., I think we'll be cutting along.

(a) care
(b) think
(c) believe
(d) mind

Business Idiom in English, Intermediate level

ESL/EFL Test #130 "Way of saying goodbye", answer 2

If you don't mind, I think we'll be cutting along.

Correct answer: (d) mind

Your answer was: incorrect
If you don't care, I think we'll be cutting along.
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What is the meaning of the phrase "To cut along"?

Issidora

[Mister Micawber]

.
To move on:

cut along (intransitive verb)

U.K. hurry off: go somewhere promptly ( dated informal ) ( usually used as a command )
.
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Native English teacher at Mister Micawber's

[Luby]

Good Evening!
So 'cutting along' means 'to move on',then is this sentence correct:I am now cutting along to my work.
Thanks!