“Stick to your knitting” means that one should concentrate (especially in business) on what one does best. The American saying “stick to your knitting” has been cited in print since at least 1826, and “mind your knitting” since at least 1829. The saying is similar to “let the cobbler stick to his last,” a saying credited to the Greek painter Apelles of Kos from the 4th century B.C.
 
“Stick to your knitting” can also be an admonishment meaning “mind your own business.”
   
   
The Free Dictionary
stick to your knitting
if a person or company sticks to their knitting, they continue to do what they have always done instead of trying to do something they know very little about
He believes the key to a company’s success is to stick to its knitting rather than trying to diversify.
       
Wikipedia: Apelles
Apelles (Ἀπελλῆς) of Kos (flourished 4th century BC) was a renowned painter of ancient Greece. Pliny the Elder, to whom we owe much of our knowledge of this artist (Naturalis Historia 35.36.79-97 and passim) rated him superior to preceding and subsequent artists.
(...)
Pliny connects a number of sayings to Apelles, which may come from Apelles’ lost treatise on the art of painting. (...) Another refers to his practice of exhibiting his works in the front of his shop, then hiding nearby to hear the comments of passers-by. When a cobbler commented on his mistakes in painting a shoe, Apelles made the corrections that very night; the next morning the cobbler noticed the changes, and proud of his effect on the artist’s work began to criticize how Apelles portrayed the leg—whereupon Apelles emerged from his hiding-place to state: Ne sutor ultra crepidam—“Let the shoemaker venture no further.”
 
Answers.com
Oxford Dictionary of Proverbs: Let the cobbler stick to his last
Attributed to the Greek painter Apelles (4th cent. bc): see quot. 1721. The ‘shoemaker’ variant is a long-standing one in British proverb lore, but is now mainly North American. A last is a wooden or metal model on which a shoemaker fashions shoes or boots. Cf. [Pliny Natural History xxxv. 85] ne supra crepidam sutor iudicaret, the cobbler should not judge beyond his shoe; [Erasmus Adages i. vi. 16] ne sutor ultra crepidam
   
21 February 1826, Franklin Post & Christian Freeman (Greenfield, MA), pg. 179, col. 1:
Don’t fret, little one—the “modest beatings” of your heart should have taught you better than to run your delicate frame among the rude buffets of “men of the iron mould”—but since you have been so imprudent, you should calmly draw instruction from your bad luck, and learn in future to stick to your knitting-work.
A. Q. F.
 
25 November 1829, New-York (NY) Evening Post, pg. 2, col. 1:
“Come, come, you mind your knitting; women know nothing about matters of government.”
 
HathiTrust.org
Horse Shoe Robinson:
A Tale of the Tory Ascendency
By John Pendleton Kennedy
Philadelphia, PA: Carey, Lea & Blanchard
1835
Pg. 67:
‘You are entirely out of my depth, brother,’ interrupted Mildred.
 
‘I know I am. How should women be expected to understand these matters? Go to your knitting, sister: you can’t teach me.’
   
16 May 1867, Cincinnati (OH) Daily Gazette, “A Homesick Adventurer—Notes of Western Experience,” pg. 1, col. 4:
Mechanics and tradesmen who are doing well in your own Eastern localities, stick to your knitting, unless you have a sure thing, for there are but few of your trades but what are well represented.
     
Google Books
28 April 1898, The Pharmaceutical Era, pg. 651, col. 2:
“STICK TO YOUR KNITTING.”
There is naturally a temptation with every advertiser to work into his advertising some of those things which are uppermost in his mind at the time of writing, or make allusions to topics which are prominently in the public mind.
(...)
There is a homely old injunction which originated in our business days which the advertiser might recall. It is this: “Stick to your knitting.”
 
16 August 1901, Miami (FL) Weekly Herald, pg. 4 ad:     
Just buy your goods from us, and stick to your knitting.
(Malone, Harned & Wade—ed.) 
 
Google Books
Brewster’s Millions
By Richard Greaves (George Barr McCutcheon)
Chicago, IL: H. S. Stone
1903
Pg. 75:
When Montgomery reached home he found this telegram from Mr. Jones.
 
Montgomery Brewster, New York City.
Stick to your knitting, you damned fool.
S. Jones.
 
21 November 1904, Lexington (KY) Herald, pg. 6, col. 5:
RUNGS IN
THE LADDER
OF SUCCESS
Advice From a “Derelict.”
(...)
Stick to Your “Knitting”!
“My advice to young business men who have accumulated some capital and are eager to better themselves,” said a guest at the Fifth Avenue Hotel to a Commercial representative, yesterday, “is to stick closely to one sort of business—not to have a lot of ‘irons in the fire’—and to make sure that they have money enough to back up their venture.”
 
OCLC WorldCat record 
My boy and I.—Stick to your knitting.—Thistle down. [Music by Herbert Stothard.].
Author: Herbert Stothard
Publisher: New York : Harms, ©1923.
Edition/Format:  Musical score : English
 
Internet Broadway Database
Mary Jane McKane (12/25/1923 - 05/03/1924)
music by Herbert Stothart and Vincent Youmans; lyrics by William Carey Duncan and Oscar Hammerstein II  
(...)
ACT 1
Song List   Sung By
The Rumble of the Subway…Ensemble
Speed…Joe McGillicudy and Cash and Carrie
Not in Business Hours…Andrew Dunn, Jr., Louise Dryer and Chorus
Stick to Your Knitting…Mary Jane McKane, Joe McGillicudy and Chorus
My Boy and I…Louise Dryer and Chorus
Toodle-oo…Mary Jane McKane and Andrew Dunn, Jr.
Down Where the Mortgages Grow…Joe McGillicudy, Maggie Murphy and Chorus
 
Google News
21 May 1927, Miami (FL) Daily News, “For Justice All the Time,” pg. 6, col. 5:
But you, Mr. Milam, why don’t you stick to your knitting? You know as well as I know, Mr, Milam, what the vital question is before Dade county at this precise moment.
   
OCLC WorldCat record
Stick to Your Knitting: Among the control supplier conglomerates, there’s less diversification, more focus on core competencies
Edition/Format:  Article : English
Publication: CONTROL ENGINEERING -HIGHLANDS RANCH- CAHNERS- 43, no. 17, (1996): 37
Database: British Library Serials
   
OCLC WorldCat record
Hi-Tech turnaround: There are two lessons to be learnt from the mis-steps made by US-based infotech company Novell - stick to your knitting and don’t let your competitors set your agenda
Author: V Jayne
Edition/Format:  Article : English
Publication: MANAGEMENT -AUCKLAND- 46, no. 5, (1999): 44-51
Database: British Library Serials
 
Forbes.com
Stick to Your Knitting
Seth Lubove, 03.01.04
After 41 years and many failed competitors along the way, HERB AND MARION SANDLER still run what is not just the U.S.’ best-managed thrift, but perhaps its best financial company. More surprising, they’re happily married after working side by side the entire time.