1630s, "tree branches cut off;" 1732, "thicket of small trees and shrubs," from brush (n.2) + wood (n.).
Entries linking to brushwood
brush n.2
"shrubbery, small trees and shrubs of a wood; branches of trees lopped off," mid-14c., from Anglo-French bruce "brushwood," Old North French broche, Old French broce "bush, thicket, undergrowth" (12c., Modern French brosse), from Gallo-Roman *brocia, perhaps from *brucus "heather," or possibly from the same source as brush (n.1).
wood n.
Old English wudu, earlier widu "tree, trees collectively, forest, grove; the substance of which trees are made," from Proto-Germanic *widu- (source also of Old Norse viðr, Danish and Swedish ved "tree, wood," Old High German witu "wood"), from PIE *widhu- "tree, wood" (source also of Welsh gwydd "trees," Gaelic fiodh- "wood, timber," Old Irish fid "tree, wood"). Out of the woods "safe" is from 1792.