Using a comma in this case is comma splicing, an error involving joining two independent clauses with a comma (but no conjunction). Had you used but (a conjunction) versus however (an adverb), comma splicing would have been avoided an your sentence would be correct.
Veterinarians suspected that the animals had died from the disease called "blackleg," but this diagnosis did not explain the condition of the bodies.
You may also present this sentence as two independent and separate, but related, thoughts that are equally important by using a semicolon and a comma:
Veterinarians suspected that the animals had died from the disease called "blackleg"; however, this diagnosis did not explain the condition of the bodies.
And, of course, you could full-stop between the clauses with a period
Any of the above is a matter of preference, but subtle differences in inferences may result. Use of the conjunction "but" appears to make this a criticism of the findings (suspicions). Using the two independent thoughts tied with a semicolon, the inference may be more mild, as if you were saying, "unfortunately" or "sadly." But, of course, if you meant no criticism of the opinions, you should probably use a word such as "unfortunately," which is also an adverb, and should be preceded by a semicolon or a full-stop period.
Final thought: Be careful of how you associate the noun "suspicions" with the noun "diagnosis;" many in the scientific or medical field may object to that implication.