Abarim Publications' online Biblical Greek Dictionary
σπενδω
The verb σπενδω (spendo) means to pour out or libate (Philippians 2:17 and 2 Timothy 4:6 only). It stems from a widely attested Proto-Indo-European root "spend-", also meaning to pour out or libate. Why PIE had a whole root for to libate isn't quite clear, but it may have had to do with a ritualistic pouring out in order to settle some sort of agreement or covenant. From this same PIE root, Latin obtained its verb spondeo, to vow or pledge, from which English got words like to respond and to be responsible. Likewise, the English words despond and desponded come from de, away from, and spondeo, pledge, and are descriptive of someone who is entirely void of anybody else's endorsements (see ασπονδος, aspondos, below).
Perhaps somewhat curiously, our English verb "to spend" does not come from this PIE root but rather from the Latin phrase expendo, from ex, out, and pendo, to weigh. Also the word "sponge" has nothing to do with our root "spend-" but rather derives from σπογγος (spoggos), sponge.
ασπονδος
The adjective ασπονδος (aspondos) means without libation, and consists of the common particle of negation α (a) and a noun derived from the verb σπενδω (spendo), to pour out or libate (see above). In the classics, this word could describe some abandoned, neglected or to be avoided deity, but more often pointed toward human parties who had not made an agreement or pact and were thus in a state of war, whether actively or tacitly. When this word was used to describe a single individual, it was to emphasize that this person was unreasonably disagreeable, implacable and uncooperative. In the New Testament, this word occurs with that latter meaning, in Romans 1:31 and 2 Timothy 3:3 only.