You would not die instantly. There are three possible causes of death when the throat is cut. The most likely is exsanguination; if the external jugular vein, and/or internal jugular vein, and/or carotid artery are cut the person will bleed to death.
external jugular vein
The external jugular vein receives the greater part of the blood from the exterior of the cranium and the deep parts of the face, being formed by the junction of the posterior division of the retromandibular vein with the posterior auricular vein.
Human anatomy (gr. ἀνατομία, "dissection", from ἀνά, "up", and τέμνειν, "cut") is primarily the scientific study of the morphology of the human body. Anatomy is subdivided into gross anatomy and microscopic anatomy. Gross anatomy (also called topographical anatomy, regional anatomy, or anthropotomy) is the study of anatomical structures that can be seen by the naked eye. Microscopic anatomy is the study of minute anatomical structures assisted with microscopes, which includes histology (the study of the organization of tissues), and cytology (the study of cells). Anatomy, human physiology (the study of function), and biochemistry (the study of the chemistry of living structures) are complementary basic medical sciences that are generally together (or in tandem) to students studying medical sciences.
In some of its facets human anatomy is closely related to embryology, comparative anatomy and comparative embryology, through common roots in evolution; for example, much of the human body maintains the ancient segmental pattern that is present in all vertebrates with basic units being repeated, which is particularly obvious in the vertebral column and in the ribcage, and can be traced from very early embryos.
Internal jugular vein
A suicide method is any means by which a person commits suicide, purposely taking his or her own life. Suicide methods can be classified according to two modes of interrupting one's life processes: physical or chemical. Physical modes of interruption typically act by incapacitating the respiratory system or the central nervous system, usually by destruction of one or more key components. Chemical modes focus on interrupting biologically significant processes such as cellular respiration or diffusion capacity. Chemical methods of suicide produce latent evidence of action, whereas physical methods provide direct evidence.]citation needed[
Suicide by exsanguination involves reducing the volume and pressure of the blood to below critical levels by inducing massive blood loss. It is usually the result of damage inflicted on arteries. The carotid, radial, ulnar or femoral arteries may be targeted. Death may occur directly as a result of the desanguination of the body or via hypovolemia, wherein the blood volume in the circulatory system becomes too low and results in the body shutting down.]citation needed[
Internal jugular vein is a paired vein collecting the blood from the brain, the superficial parts of the face, and the neck. An internal jugular vein is a type of jugular vein.
On both sides and at the base of the brain, the inferior petrosal sinus and the sigmoid sinus join to form the internal jugular vein. The internal jugular vein begins in the posterior compartment of the jugular foramen, at the base of the skull.
Common carotid artery
The jugular veins are veins that bring deoxygenated blood from the head back to the heart via the superior vena cava.
In human anatomy, the left and right common carotid arteries (English pronunciation: //) are arteries that supply the head and neck with oxygenated blood; they divide in the neck to form the external and internal carotid arteries.
The common carotid artery is a paired structure, meaning that there are two in the body, one for each half. The left and right common carotid arteries follow the same course with the exception of their origin. The right common carotid originates in the neck from the brachiocephalic trunk. The left arises from the aortic arch in the thoracic region. The bifurcation into the external and internal carotid arteries occurs at the upper border of the thyroid cartilage, at around the level of the fourth cervical vertebra (C4.)
Common facial vein
Dhabīḥah (or zabiha, Arabic: ذَبِيْحَة dhabīḥah IPA: [ðæˈbiːħɐ], 'slaughter'(noun)) is, in Islamic law, the prescribed method of ritual slaughter of all animals excluding locusts, fish, and most sea-life. This method of slaughtering animals consists of a swift, deep incision with a sharp knife on the throat, cutting the jugular veins and carotid arteries of both sides but leaving the spinal cord intact.
The anterior facial vein usually unites with the posterior facial vein to form the common facial vein, which crosses the external carotid artery and enters the internal jugular vein at a variable point below the hyoid bone.
From near its termination a communicating branch often runs down the anterior border of the Sternocleidomastoideus to join the lower part of the anterior jugular vein.