Your ABO blood type tells you which antigens of the ABO blood group are present on your red blood cells. The function of the A and B antigens are not known, but they are not essential, individuals without those antigens are healthy1.
The ABO blood type has an effect on blood clotting1, but there is no reliable evidence that it has an effect on metabolism. This does not mean that such a mechanism is impossible, but the burden of proof lies with Dr. Peter D'Adamo to provide evidence for his claims.
I could not find any clinical trials that would support this claim on his website, there are some scientific papers listed there, but those are just reviews of the literature. The Mayo clinic agrees, that there is no evidence for this claim,
There's also a recent study in PLOS One examining the blood type diet directly, and it found that there is no basis for it. The diets themselves provide some benefit, but that benefit is entirely independent from the blood type of the person:
Adherence to certain ‘Blood-Type’ diets is associated with favorable
effects on some cardiometabolic risk factors, but these associations
were independent of an individual's ABO genotype, so the findings do
not support the ‘Blood-Type’ diet hypothesis.
 Dean L., Blood Groups and Red Cell Antigens [Internet]., Bethesda (MD): National Center for Biotechnology Information (US) (2005).