“Don’t let the tax tail wag the investment dog” (sometimes given as simply “dog” or “profit dog” or “savings dog"or “economic dog”) means that one shouldn’t let taxes solely drive business decisions. An investment should be bought or sold on its merits, with taxes being the last consideration.
 
The expression “tail wag the dog” is cited in the 19th century; “tax tail wag the dog” is cited from the 1960s.
 
   
13 September 1965, Appleton (WI) Post-Crescent, “State Bank Women Convene Here,” pg. A14, col. 7:
Consider Tax Last
Mr. Nehs cautioned that one should not let the tax tail wag the whole dog. One should decide where and how he wants his money to go and then let his attorney or accountant handle the tax question.
(Franklin Nehs, an Appleton attorney—ed.)
   
Google Books
Estate Planning and the Close Corporation
By Jerome A. Manning and Selma Arnold
New York, NY: Practising Law Institute
1970
Pg. 338:
Again, these tax factors have to be weighed against what you really want to do with the property. Do not let the tax tail wag the intent dog.
   
5 November 1975, Traverse City (MI) Record-Eagle, “Don’t miss dependent deductions” by Sylvia Porter, pg. 21, col. 3:
Don’t let the tax tail wag the economic dog.
   
Google Books
Major Tax Planning
By University of Southern California (John W Ervin, Louis Morris Brown)
Published by Matthew Bender
1978
Pg. 218:
In no event should the “tax tail wag the dog,” ...
 
17 December 1981, Doylestown (PA) Daily Intelligencer, “Heed critical dates for making stock market moves” by Sylvia Porter, pg. 32, col. 3:
BEST TAX ADVICE OF ALL: Keep your year-end tax sales in proper perspective. Taxes should not be your dominant consideration in investment decisions. Never let the tax tail wag the investment dog.
     
Google Books
Encyclopedia of Investments
By Marshall Blume and Jack P. Friedman
Published by Warren, Gorham & Lamont
1982
Pg. 743:
It is always easy to let the tax tail wag the investment dog. There are many attractive tax reasons to invest in farmland, but the investor should not lose…

13 September 1982, Syracuse (NY) Herald-Journal, “Your Money’s Worth” by Sylvia Porter,  pg. C6, cols. 4-5:
But don’t let the tax tail wag your investment dog. If you have decided that your stock has reached its top price, you’re almost certainly better off selling right now—even if it’s a short-term capital gain instead of a favorably taxed long-term capital gain.
     
Google Books
Personalized Guide to Financial Planning
By Charles J. Felmeister, Thomas L. Snyder and Michael M. Tulman
Published by C.V. Mosby Co.
Item notes: v.5
1983
Pg. 54:
An old tax planning adage, “Don’t let the tax tail wag the investment dog,” should not be forgotten. Tax aspects of an investment should be part of the considerations when evaluating an investment but rarely the sole reason for making the…
 
20 April 1989, Boston (MA) Globe, “Now that taxes are done, let’s talk taxes” by Hank Gilman:
Rule of thumb, however: Don’t let the tax tail wag the investment dog.