Can I play MP3 without connecting Samsung DVD player to the TV?

Yes, generally Samsung DVD player requires TV to play Mp3 sound output. But some have Inbuilt amplifier with jacks for sound output. To play Mp3 without TV you need external speakers. Attach them to your DVD's audio out ports. Speakers can be purchased from market but according to the built in amplifier capacity of your DVD Player.

( Rear side of DVD )

Some DVD player does not have sound output port and built in amplifier, in such cases you need speakers with Built in amplifier (amplifier according to your requirement). That needs to be connected to your DVD player using Microphone Jack in your DVD player.