How to use Sub and GetAtt functions at the same time in CloudFormation template?

You don't need to use !GetAtt here, !Sub will automatically unpack values for you if you place them within the place holder:

Uri: !Sub arn:aws:apigateway:us-east-1:lambda:path/2015-03-31/functions/${TestLambda.Arn}/invocations

This is explained in the docs:

If you specify template parameter names or resource logical IDs, such as ${InstanceTypeParameter}, AWS CloudFormation returns the same values as if you used the Ref intrinsic function. If you specify resource attributes, such as ${MyInstance.PublicIp}, AWS CloudFormation returns the same values as if you used the Fn::GetAtt intrinsic function.

I know it's an old question, but still the first result in Google:

Parameters:
  path:
    Type: String
    Default: something/script.sh
Resources:
  Bucket:
    Type: AWS::S3::Bucket
Outputs:
  ScriptUrl:
    Description: Script Url
    Value:
      Fn::Sub:
        - ${url}${the_path}
        - {url: !GetAtt Bucket.WebsiteURL, the_path: !Ref path}