The Bible records no such prohibition. Some have misunderstood Deuteronomy 23:17-18 to say that the price of dogs should not be brought into God's house. Notice: "You shall not bring the hire of a harlot or the price of a dog to the house of the LORD your God for any vowed offering, for both of these are an abomination to the LORD your God."
The Hebrew word for dog in this verse means "a male cult prostitute" (see Brown, Driver & Briggs Hebrew Lexicon). Verse 17 shows that the context is religious rites that involve sexual acts, as was anciently common among many idolatrous peoples: "There shall be no ritual harlot of the daughters of Israel, or a perverted one of the sons of Israel." The Moffatt and other modern versions make it clear that these verses are speaking of sexually corrupt people.
The New Testament records something similar in Revelation 22:15: "But outside are dogs and sorcerers and sexually immoral. . . ." This refers to various categories of unrepentant and degenerate humans who will be unable to enter God's Kingdom.
Literal dogs, on the other hand, are merely a part of the animal creation, which God has given man dominion over (Genesis 1:26). To tithe the income from the sale of a dog or any other animal is in accord with God's tithing laws and principles.