When using the spell astral projection, you gain a vulnerability: If your silver cord is severed, you die:
If the cord is cut--something that can happen only when an effect specifically states that it does--your soul and body are separated, killing you instantly.
However, this can only happen if an effect specifically states it can do so. An example of this is the silver longsword of the githyanki knight, which states that it can sever a silver cord on a crit.
On a critical hit against a target in an astral body (as with the astral projection spell), the githyanki can cut the silvery cord that tethers the target to its material body, instead of dealing damage.
However, the rare magic item adamantine armor states that
any critical hit against you becomes a normal hit.
Does this make it so that this type of effect cannot sever your silver cord?