Any ideas on the origin of the 绍 character?
The real way to describe characters should only utilise a surface level, not recursive, decomposition.


「紹」originally meant to continue. The meaning introduce is a semantic extension from to continue > to bring two things together > to introduce.
「紹」is made from semantic「糸」(silk threads) and phonetic「召」(zhào or shào).


「糸」as a semantic component, sometimes in an abbreviated form「幺」, appears in many characters to do with linking, continuation, such as「繼」(to continue),「續」(to join together),「系」(to tie, link > system, series), 「斷」(to break),「胤」(offspring).
「召」is comprised of phonetic「刀」(dāo) and semantic「口」(mouth), and originally meant to beckon, call, summon. There was originally no meaning connection between「召」and「紹」; any connection between to call and to introduce is coincidental, but you can utilise this connection as a mnemonic.
Other characters using「召」as a phonetic component include 招昭炤沼詔邵韶.「召」, like many other components used as a phonetic, may not contribute any semantic value to the whole character.