Is it permissible to slaughter part of a buffalo with the intention of fulfilling a vow that was to slaughter a sheep, while benefiting from the remainder of the buffalo's price?

What that person told you about selling the vowed sheep was not correct. Rather, you should have slaughtered it to fulfill your vow, because a specified vowed item cannot be sold or exchanged for anything less valuable, as confirmed by Ibn Uthaymeen. You must repent and seek forgiveness, and guarantee the sheep by slaughtering a similar one or one of greater value, and then giving it in charity to the poor and needy.

If the price at which you sold the vowed sheep exceeded the value of the replacement sheep, then the surplus is a vow, and you are not permitted to benefit from it. Al-Nawawi, in his commentary on Al-Muhadhdhab, mentioned three possibilities regarding this surplus: either you contribute it to another sacrifice, or you buy meat with it and give it in charity, or you give the money itself in charity.