“Mutton-chop whiskers” are sideburns (extending into a bead) that look like a pair of mutton chops on the side of a man’s face. The term “mutton-chop whiskers” was printed in the New-York (NY) Daily Tribune on October 24, 1851, in a report from London.
 
     
Wiktionary: mutton-chop whiskers
Etymology
From the shape of a muttonchop
Noun
mutton-chop whiskers (uncountable)
1. sideburns that are narrow near the ear and broad and rounded near the chin
 
(Oxford English Dictionary)
mutton chop, n.
Usually in plural. A man’s sideburn shaped like a mutton chop, being narrow at the ear and broad and rounded at the lower jaw. Frequently attributive (usually with hyphen), esp. in mutton-chop whiskers.
[1851   Internat. Mag. Lit., Art, & Sci. July 447/2   Their stiffness of bearing,..their hair, their whiskers cut into the shape of mutton chops..all that makes them as proud as Trafalgar and Waterloo.]
1855   Putnam’s Monthly Mag. June 562/1   Have we not all seen that Milor..sporting jacket with large buttons, his mutton-chop whiskers, and rosy, moony face?
1857   Harper’s Weekly 4 Apr. 212   The English mutton-chop whisker, growing on the bluff cheeks of the Briton, explains the carbonaceous character of the islander.
     
Newspapers.com
24 October 1851, New-York (NY) Daily Tribune, pg. 6, col. 2:
FROM NEW YORK TO NINEVEH.
PEOPLE AND THINGS IN LONDON.
(...)
Great numbers of foreigners, principally French and German, are now in the city, and the people are so accustomed to see heavy beards and ferocious moustaches, instead of smooth chins and mutton-chop whiskers, that a little deviation from the ordinary English standard of dress and appearance, attracts no attention.
 
Newspapers.com
4 November 1854, Thibodaux (LA) Minerva, pg. 3, col. 6:
MUTTON-CHOPS AND WHISKERS.—The London Quarter attributes the origin of the national English whisker to the Netional English mutton-chop. Thus the reviewer connects them:
 
“A mutton-chop suggested the form of a substantial British whisker. Out of this simple countless varieties have arisen; one has whiskers turned into the corners of his mouth, as if he was holding them up with his teeth; the second had wandered into the middle of the cheek, and there stopped, as though it did not know where to go, like a youth who has ventured out into the middle of a ballroom, with all eyes upon him; another twists the contrary way, under the owner’s ears; another, with a vast Pacific of a face, has little whiskers, which seem to have stopped shart after two inches of a voyage, as though aghast at the prospect of leaving to turn such a Cape Horn of a chin. We perceive coming a tremendous pair, running over his shirt-collar in luxuriant profusion; yet we see, as the colonel or general takes off his hat to a lady, that he is quite bald; those whiskers are, in fact, nothing but a tremendous landslide from the veteran’s head.”
 
Google Books
The Detective’s Note-Book
Edited by Charles Martel
London, UK: Ward and Lock
1860
Pg. 95:
“Five months and seven days after the publication of this second notice, on returning from my shop, I found a well-dressed, rather handsome young man, with shining black hair, and mutton-chop whiskers of the same hue, waiting for me at my rooms.”
 
YouTube
Beard Styles: How to Shave Mutton Chops Beard | Gillette
Published on Dec 9, 2013
Gillette
Wondering how to trim sideburns? Learn how to shave your beard into some really cool looking mutton chop sideburns. To find the best shaving products to style your beard, click here: http://gillette.com/en-us/products/ra...
   
Beardoholic
Ultimate Mutton Chops (Sideburns)
by Zack Robbins | Last updated Jul 15, 2019 | Beard Styles, Beardoholic
Perhaps you are looking for a style of facial hair that is fun and will definitely have you standing out in the crowd.
 
If this sounds like you, then the mutton chops just might be the perfect new beard style for you.
 
This classic look still holds its powerful dominance even in the fashion world, drawing attention first to your face and then what you might be wearing.