Methods of sealing a hydrocarbon well containing a control line. The hydrocarbon well includes a casing string extending within a wellbore and defining a casing conduit, production tubing extending within the casing conduit and defining a tubing conduit, and at least one control line extending within an annular space. The methods include fluidly isolating a downhole region of the tubing conduit from an uphole region of the tubing conduit and actuating a shape charge device. The actuating includes forming a plurality of openings within the production tubing and severing the at least one control line. The methods also include positioning a diversion structure within the uphole region of the tubing conduit, pumping a sealing material into the annular space at the sealing material injection region, and curing the sealing material to form a fluid seal that extends within the annular space and the uphole region of the tubing conduit.