'To cut one's stick' definitions:

Definition of 'To cut one's stick'

From: GCIDE

Stick \Stick\, n. [OE. sticke, AS. sticca; akin to stician to stab, prick, pierce, G. stecken a stick, staff, OHG. steccho, Icel. stik a stick. See Stick, v. t..]
1. A small shoot, or branch, separated, as by a cutting, from a tree or shrub; also, any stem or branch of a tree, of any size, cut for fuel or timber. [1913 Webster]
Withered sticks to gather, which might serve Against a winter's day. --Milton. [1913 Webster]
2. Any long and comparatively slender piece of wood, whether in natural form or shaped with tools; a rod; a wand; a staff; as, the stick of a rocket; a walking stick. [1913 Webster]
3. Anything shaped like a stick; as, a stick of wax. [1913 Webster]
4. A derogatory expression for a person; one who is inert or stupid; as, an odd stick; a poor stick. [Colloq.] [1913 Webster]
5. (Print.) A composing stick. See under Composing. It is usually a frame of metal, but for posters, handbills, etc., one made of wood is used. [1913 Webster]
6. A thrust with a pointed instrument; a stab. [1913 Webster]
A stick of eels, twenty-five eels. [Prov. Eng.]
Stick chimney, a chimney made of sticks laid crosswise, and cemented with clay or mud, as in some log houses. [U.S.]
Stick insect, (Zool.), any one of various species of wingless orthopterous insects of the family Phasmidae, which have a long round body, resembling a stick in form and color, and long legs, which are often held rigidly in such positions as to make them resemble small twigs. They thus imitate the branches and twigs of the trees on which they live. The common American species is {Diapheromera femorata}. Some of the Asiatic species are more than a foot long.
To cut one's stick, or To cut stick, to run away. [Slang] --De Quincey. [1913 Webster]