Can I pursue B.Sc in chemistry after completing Diploma in mechanical engineering?

No, you need PUC passing certificate to go for degree in B.Sc, and that too with minimum 50% marks in you academics.

Dear, If you have done your DME after + 2, and if you have completed +2 with PCM then on the basis of +2 results, you can apply for B.Sc in chemistry. Yes, Mr. Chandrakant rightly pointed out that this type of switching may not be helpful and result oriented for career building. Better you may be be

No, it is not possible to get admission on the basis of Diploma in mechanical. As you did your Diploma in mechanical, you would have taken admissions in it after thinking to make career in mechanical, so I suggest you to go ahead in the same field rather than switching from one domain to another.