Grading of the chain: This chain is weak because Abbad bin Mansur is weak, and he was inconsistent in it (sometimes narrating it as marfu', sometimes as mawquf), and he is also a "mudallis".
Technical note: Abu Hatim al-Razi says (in "al-Jarh wa al-Ta'dil" 6/86): "We think he took these hadiths from Ibrahim bin Abi Yahya, from Dawud bin al-Husayn, from Ikrimah, from Ibn Abbas." We say: This means he would commit tadlis with them by dropping two men: Ibrahim bin Abi Yahya, who is "matruk al-hadith", and Dawud bin al-Husayn, who is "weak" in his narration from Ikrimah.

Reference / Source: Al-Bayhaqi (8/233) narrated it via Muhammad bin Ya'qub, from Yahya bin Abi Talib, with this same chain.

Reference / Source: Al-Tabari narrated it in the Musnad of Ibn Abbas in "Tahdhib al-Athar" (1/550) via Awn bin Umarah, and al-Bayhaqi (8/232) via Abd Allah bin Bakr al-Sahmi; both of them from Abbad bin Mansur, with this same chain.
Addition: They added in it: "and the one who does it and the one to whom it is done in sodomy (kill both), and kill everyone who has intercourse with a woman of prohibited degree (mahram)."

Reference / Source: Ahmad (4/2733) narrated it from Abd al-Wahhab bin Ata', with this same chain, as "mawquf" (on Ibn Abbas).

Reference / Source: Al-Tabari (1/551) also narrated it as "mawquf" via Yazid bin Harun, from Abbad bin Mansur, from "al-Hakam", from Ibn Abbas. (Here) the name Ikrimah is corrupted into "al-Hakam", whereas the correct name comes in Ibn Abi Shaybah (10/104) with another part of the hadith. Ibn Abi Shaybah (10/8), al-Tahawi in "Sharh al-Mushkil" (3831), al-Tabarani in "al-Kabir" (11568), al-Daraqutni (3236) and al-Bayhaqi (8/324) narrated it via Ibrahim bin Isma'il bin Abi Habibah, from Dawud bin al-Husayn, from Ikrimah. Al-Tabarani, al-Daraqutni and al-Bayhaqi added: "killing the one who has intercourse with a woman of prohibited degree."
Grading of the chain: Its chain is weak; it will be discussed at number (8253), where the author (al-Hakim) will cite another part of it via this same Ibrahim bin Isma'il bin Abi Habibah, and its sources will come there.

Analysis: As for the route of Ibrahim bin Abi Yahya al-Aslami to which Abu Hatim al-Razi pointed, it was narrated by Abd al-Razzaq (13492), and likewise by al-Tabarani in "al-Kabir" (11569) and Ibn Adi in "al-Kamil" (1/222), and through him al-Bayhaqi (8/232), via Ibn Jurayj; both of them (Abd al-Razzaq and Ibn Jurayj) from Ibrahim al-Aslami, from Dawud bin al-Husayn, with this same chain.