Should I report a 48th percentile math GRE subject exam score for programs where it's optional? I recently received my Mathematics GRE subject test score of 650 ( 48%). I know this score is miserable but in my country, I have the option to retake the GRE next year October only.

Assuming otherwise I have a strong profile (with achievements in other examinations in my country and some research experience ) Should I be reporting this score to universities where it is not mandatory (but highly encouraged) to submit Math subject GRE scores? I mean will this score weaken my application?

Before this score, I was thinking of applying to universities like Upenn, Penn State etc but feel really nervous about my admission prospects now..
Since the admissions office receive applications in large numbers they would prefer to work the application that corresponds to the "required list", otherwise it would delay the process. Sending in documents, in your case a low subject score, could have an adverse effect on your application. If the application does not require a subject score, do not send a weak subject score as it will not make your application stronger.

There is a GRE general test and subject test. As far as i know, the general test is mandatory for most programs, but the subject test is optional. 

General rule: do not send anything that is optional and does not strengthen your application.