'sap-producing' is a modern English compound formed from 'sap' (Old English 'sāp') and the present participle of 'produce' (from Latin 'producere' via Old French and Middle English).

'sap' comes from Old English 'sāp' meaning 'juice' or 'sap', while 'produce' comes from Latin 'producere' (through Old French and Middle English); the compound 'sap-producing' is a straightforward 20th/21st-century English formation combining these elements.

Initially the component words meant 'plant juice' ('sap') and 'to lead forth'/'bring forth' ('produce'); combined as 'sap-producing' the meaning is simply 'producing sap' and has remained literal and unchanged.