Will paramedics stitch up a stab wound on the spot or wait till the hospital?

Paramedics: Are not authorized (though some certainly are capable) of suturing wounds. That is the territory of physicians and their authorized and appropriately trained mid-level providers.

Dressing only: Some advance practice paramedics (like Tactical EMS providers) or military medics in a military setting can close wounds primarily with suture/glue/staples. Otherwise, they stop the external bleeding, cover wound and apply dressing until in ER.