It seems that your quote is a part of a longer hadith which can be found in Musnad Ahamd (Musnad al-Ansar on the authority of abu Ummamah) and in at-Tabarni's al-Mu'jam al-Kabir. Abu Bakr al-Haythami quoted it in his majma' az-Zawaaid مجمع الزاوئد ومنبع الفوائد without giving a qualification.
So yes the hadith exists. However both narrations I could explicitly find use the wording "a mercy and guidance for mankind رحمة وهدى للعالمين" instead of " a guidance and mercy believers هدى ورحمة للمؤمنين".
You will certainly not find this hadith in sunan abi Dawod as-Sijistani, as the abu Dawod whom apparently compiled it is abu Dawod at-Tayalisi a scholar who actually died when the author of as-Sunan was about 2 years old. Other compilers seem to be al-Ajuri in his Taḥrīm al-nard wa-al-shiṭranj wa-al-malāhī and ad-Daraqutni in his 'ilal al-hadith according this thread on ahlalhadeeth.com.
Let's move now to the narrator chain of imam Ahmad (and the beginning of the chain of at-Tabarani, but the common part seems enough for a qualification):
يزيد أنبأنا فرج بن فضالة الحمصي عن علي بن يزيد عن القاسم عن أبي أمامة
Yazid -ibn Haron- (at Tabarani here has narrated from an other narrator who is rather discussed among scholars)-> Faraj ibn Fadala al-Himsi -> 'Ali ibn Yazid -> al-Qasim -> Abu Umamah
Faraj ibn Fadala al-Himsi is considered as rejected (munkar al-Hadith).
'Ali ibn Yazid is also considered as rejected.
So that some say this hadith seems to be fabricated.
Ibn Hebban said (in his book al-Majrooheen):
قال ابن حبان((وإذا اجتمع في إسناد خبرٍ عبيدُ الله بن زحر وعلي بن يزيد والقاسم أبو عبد الرحمن، لا يكون متنُ ذلك الخبر إلاَّ مِمَّا عملت أيديهم
... if in the chain of narration (news) you find Obaydallah ibn Zahr and 'Ali ibn Zayd and al-Qasim ibu Abdarrahman, then the content of this narration (news) can't be but made by their hands (fabricated)
This statement appears even stronger if we take into consideration that many scholars hold the opinion that ibn Hebban is among the rather lenient scholars of al-Jarh wa-Ta'adeel.
One of the chains ad-Daraqutni quoted indeed quotes 'Obaydallah ibn Zahr (a narrator he himself qualify as not so strong, while he says his master/sheikh 'Ali is a rejected narrator).
Sheikh Sho'aib al-Arnaut considers this hadith as da'if jiddan (very weak).
Mulla 'Ali al-Qari wrote a hadith interpretation on a shortened version of this hadith in his mirqat al-mafatih sharh meshkat al-Masbih.