Jesus had issues both with breathing on the cross and he lost blood from the crown of thorns, scourging, and nails in his hands and feet. Asphyxiation is one reason commonly proposed, but most likely it was a combination of loss of blood and breathing issues for the cause of his death.
Jesus of Nazareth underwent Jewish and Roman trials, was flogged, and was sentenced to death by
crucifixion. The scourging produced deep stripelike lacerations and appreciable blood loss, and it probably
set the stage for hypovolemic shock, as evidenced by the fact that Jesus was too weakened to carry the
crossbar (patibulum) to Golgotha. At the site of crucifixion, his wrists were nailed to the patibulum and,
after the patibulum was lifted onto the upright post (stipes), his feet were nailed to the stipes. The major
pathophysiologic effect of crucifixion was an interference with normal respirations. Accordingly death
resulted primarily from hypovolemic shock and exhaustion asphyxia. Jesus’ death was ensured by the thrust
of a soldier’s spear into his side. Modern medical interpretation of the historical evidence indicate that Jesus
was dead when taken down from the cross.
It apparently was the custom of the Jews to wash off blood.
Normally yes. But as I’ve pointed out, there are exceptions to this as evidenced by Jewish sources.
(As a side note, not dying of blood loss is one of the reasons Jesus didn’t qualify as a sacrifice. The Paschal sacrifice had to die of blood loss.)
I’m not so sure the sacrifices had to die simply because of blood loss, instead, the death was initiated by cutting the throat, so there’s both loss of breathing and loss of blood.