Translated straight from English it would be: "Lo sai che sono stanco/ho sonno... ho tanto sonno che mi sento come se dovessi morire." [you know that I am tired/sleepy, I am so sleepy that I feel like I am going to die]. But this is very redundant and does not really show "death" in a metaphorical way.
Indeed, we have an two expressions for that, which are: "sono stanco morto" = "I´m dead tired" and "Ho sonno da morire" = (litt. "I´m sleepy to die"), I´m sleepy like hell. They are very common and very effective.
Your sentence will be: "Lo sai che stanco. Ho (proprio) sonno da morire!"
[I used stanco (tired) and avere sonno (to be sleepy), because the Italian language avoids repeating words. In any case you could also say "Lo sai che ho sonno.
Ho proprio sonno da morire!" or, to make it sound less redundant "Lo sai che ho sonno. Anzi, ho sonno da morire!" = You know I´m sleepy. Nah, I´m rather sleepy like hell!"]