Mazda problem
 

Hey guys coming here to look for some help. This is about my daily commuter, Mazda 3 hatchback as my rx8 is away for winter. Anyways, my hatchback is doing some weird things. If I'm in first gear and let off clutch it will sometimes die. Engine won't stall but I'll loose raido and power steering for a split second and it will come back, but it will happen constantly over and over again untill I start going faster. I have had many manual cars and never had anything like this happen before so I'm very confused. Wondering if possibly anyone knew why this would happen.
thanks!

Check the battery cable connections. Either dirty or loose. The radio dropout is a pretty good sign.

Maaaaybe alternator connections or the alternator itself is on its way out. When you're starting out in 1st and lug the engine, it's not turning fast enough to provide stable current, but in that case the battery should be powering everything. So check/clean them battery posts first.

+1^
Also check your ground wires, especially if your DD is exposed to road salt.
They will corrode and work loose.

Hey Loki, thanks for replying, it usually only happens in traffic or if I'm slowly cruising. I will definitely check battery connections as that was my first thought. Also, thought of alternator but praying just battery. It won't start in super cold temperatures, which makes me believe something could be wrong with battery. I just bought it less than a month ago and still have the bumper to bumper warranty from dealership, so worst comes to worst, I take it back and get them to replace alternator. Wanted to see if it was a problem I could personally deal with before having to take it to dealership and loose it for x amount of time. Anyways, appreciate the response I'll definitely look into battery connections. Thank-you!

Agree with Loki.
If I were you I will first check the battery and its connection, see if there's any corrosion or rust, be sure to clean them if there are.
I'll then check the alternator, the alternator will be providing the electrical power once the engine started, however if that's on it's way out, it might not be able to provide stable current and voltage. You may choose to give more gas when letting off the clutch to force the alternator spin faster (Since it is connected to the crankshaft or the E-shaft). Also you can have open your low or/and your high beam, to see if they got darker or even being cut off.

Thanks man! Going to check battery connections tonight. Little update, today was MUCH worse as it happened while I was going 60km through town. Lost steering and when I tried to pull over it came back and almost crashed as I was forcing wheel to right. Super pissed off. I'm starting to believe it's an alternator issue but crossing my fingers that's it's battery.

If it's the battery, go to an auto store where they can load test your battery for free.

Goes without saying, but yeah, don't drive it around too much...