Green’s Dictionary of Slang

1. anyone who has suffered a prison haircut or has excessively short hair; thus attrib.

1827		‘An Officer of the Line’ Military Sketch-book I June c.100: The white [i.e. powdered, long-haired] heads which, like snow-balls, were melted away by the warmth of croppy inlfuence.
1857		‘Ducange Anglicus’ Vulgar Tongue.
1863		Criminal Life (NY) 19 Dec. n.p.: The miserable [...] woman we have appropriately designated ‘Croppy Louise’ on account of the loss of her hair.
1864, 1867, 1870		Hotten Sl. Dict.

2. a Presbyterian [as well as their chosen haircuts, they also might have their nose and/or ears cropped in a judicial punishment].

1788, 1796		Grose Classical Dict. of the Vulgar Tongue (2nd, 3rd edn) n.p.: croppie A nick name for a presbyterian: from their cropping their hair, which they trimmed close to a bowl-dish, placed as a guide on their heads; whence they were likewise called roundheads.
1811		Lex. Balatronicum.
1823		Egan Grose’s Classical Dict. of the Vulgar Tongue.
1824		Pierce Egan’s Life in London 19 Sept. 6/2: ‘Didn’t ye begin telling me ye were a serjant that helped smash the croppies all over ould Ireland?’.
1873		Sl. Dict. 133: Croppie a person who has had his hair cut, or cropped, in prison. Formerly those who had been cropped (i.e., had their ears cut off and their noses slit) by the public executioner were called croppies, then the Puritans received the reversion of the title.
1883		Dly Gaz. for Middlesbrough 10 Oct. 3/3: So with pikes and with banners / We marched to tache manners, / To Ribbonmen, Croppies, and — Papists, in fine.
1909		J. Ware Passing Eng. of the Victorian Era 99/1: Croppie (Scottish). Equivalent of Roundhead, and used precisely in the same way. Strangely enough, in the 1798 Irish rebellion, the rebel Irish were called croppies, equally from the shortness of their hair. A Hanoverian song was popular, called ‘Croppies, lie down,’ which suggestion of treating them as dogs made the rebels very wild.
1997		Share Slanguage.

3. (US Und.) a prison barber.

1935

A.J. Pollock Und. Speaks 27/2: Croppie, a barber (prison).