Why is SubtleCrypto API generating different signature for same data?
Now the problem I am facing is the signature produced by the API is
  different for the same private key and data, which should never be the
  case.


Actually in cryptography we don't require our signature schemes to be deterministic. It can even be harmful if you consider things like fault attacks (example attack PDF). Additionally you are using ECDSA which has only "recently" seen a deterministic variant in RFC 6979 and for which most standards (still?) mandate the non-deterministic variant (eg FIPS 186).

Additionally more often than not if you want to do something with deterministic signatures you are looking for a different primitive and probably should describe the problem and not the problem of "the" fix.

If you really don't want a deterministic signature scheme supported by the API you linked to, you can use RSASSA-PKCS1-v1_5 which is an older, still secure deterministic RSA-based signature scheme.