Killing a spider is the entanglement dream resolved — read as a web broken by decision: in the East a scheming matter ended, in the West a devouring pattern confronted, in Ibn Sirin's tradition a weak enemy dispatched — with one tradition's caution about what the spider also weaves.
Three readings
In Chinese tradition · 周公解梦
The Chinese frame reads the spider's death as the web's end: a scheming matter, a slow entanglement, or a patient rival dispatched by your own hand. Classical readings note the relief the dream carries — threads that held you cut at the center. One caution survives in the lore: the spider is also the weaver of what comes to you on its thread, so be sure what you killed was the trap and not the luck.
Psychologically, killing the spider is confronting the entangling pattern at its center — the controlling dynamic, the web-spinning anxiety, the relationship that fed on what it held. The act reads as decision: what was tolerated is ended. As with all dream-killings, Jung would ask one honest question after the relief — whether the spider was truly the pattern, or the patient, weaving part of yourself you have not learned to live with.
Ibn Sirin read the spider as a weak enemy in the frailest of houses — and killing it as dispatching such a foe: an insidious opposition ended with less effort than its web suggested. As meaning: the entanglement that looked formidable has been, or can be, broken — the tradition's reading is almost congratulatory, and its counsel is simply not to rebuild the web out of habit.
Mostly good: the classical readings take it as an entanglement or weak enemy ended. The cautions are minor — be sure it was the trap you ended, and don't respin the web by returning to the pattern.
What if more spiders appear after I kill one?
Multiplication after the kill reads as the pattern, not the spider, being the problem — one entanglement ended while its source keeps weaving. The dream asks for the systemic fix, not another shoe.
What does being unable to kill it mean?
The unkillable spider marks an entanglement decision not yet truly made — swatting at a pattern while staying inside its web. The dream usually resolves when the waking-life thread is actually cut.
This is the general reading. Your dream is specific.