I can't seem to beat Shadow Mitsuo. I need tips on this fight. I can take out 'Hero Mitsuo' and I know Shadow Mitsuo can summon him again. I'm having trouble when he casts that fear spells and takes out my party in a hit. I'm also playing in beginner. :/

Party Stats:
Hector: 39
Yosuke: 39
Chie: 39
Yukiko: 39

What level is your Sun Social Link at? You can fuse Yatagarasu at level 40 and he learns Null Fear at level 43. If the Sun Social Link is high enough, you can get him up to 43 fairly quickly.
Always get rid of fear after he casts it. Shadow Mitsuo has an attack that kills everyone with the fear ailment, and it never fails. But get rid of fear and that problem goes away.

What about preventing him from summoning 'Hero Mitsuo'?

Can you get some bravery vessels to equip on your party?  If you can buy some that will help a great deal.

"What about preventing him from summoning 'Hero Mitsuo'?"

Just took him out. I equipped everyone with bravery vessels. Yukiko dealt with the fear when it hit with 'Me Patra'

I just used pure power on this boss. I fused to get Black Frost and then i would boost my attack to max levels. Then hit it with Agidyne.... i was doing somewhere near 600 damage a pop on that. Established Yukiko as my healer, Chie as my booster (tarakuja), and Kanji just handled some extra physical damage (occasionally boosting the main character's defense when I predicted a hard hitting move was coming.
Black Frost was an especially effective persona because it absorbs fire, and more importantly for Mitsuo's Shadow, Ice. It made my battle incredibly easy.

Just be equipped with some Sedative (I think), and use if needed.