Several points need to be made.
The performance of the whole optical stack is incredibly resilient w.r.t. small spots on the primary mirror. The mirror might look visually very, very dirty, but the performance of the whole instrument will remain essentially the same. Even if you chip the mirror at the edge, it shouldn't matter. Take a marker and scribble a dozen lines on the mirror - it doesn't make a large difference for performance, not greater anyway than what the 4 vanes of the secondary mirror already do (we can start a separate discussion about diffraction artifacts from spots and lines on the mirror - but the bottom line is, don't worry about it).
With that in mind, you should be conservative when deciding to clean the mirror. Let it accumulate some amount of dirt, the scope will be okay.
2. Permanent damage
That being said, mold or other living things may chemically corrode the mirror. Again, a few spots of corrosion do not impact performance, but you don't want to allow this process to continue.
Dust will generally not corrode the mirror. Salt (from ocean breeze) will usually corrode it in time. With mold it's hard to say, but it's best if it's removed.
Mold grows because the mirror is wet. The mirror fogs up usually when you bring the scope back into a warm room from outside; the mirror is cold, and water in the warm air condenses on it.
Procure a cheap, small fan, and point it at the rear end of the scope while it's warming up after you bring it back in. The air current will reduce water condensation on the mirror. Turn the fan off after 30 ... 60 minutes.
Also, keep the OTA (the big tube of the telescope) capped off while not in use. This will reduce dust deposits, and therefore mold will find less food to grow. At least cap off the top end and store the scope in a vertical position; that will reduce dust deposits greatly. The bottom end is less important.
Avoid storing the scope in a place with large day/night temperature variations. When the mirror is colder than air, condensation may form. This can happen spontaneously with scopes stored in a shed outside. The mirror fogs up in the morning, when air is getting warmer but the scope is still cold. This is much less of an issue with small scopes, but it's something to keep in mind.
You could cap off both ends while in storage, and place a bag of silica gel inside the OTA (don't drop it on the mirror). That will suck up all humidity inside the OTA, but you have to bake the silica gel in the oven every so often to keep it working effectively. You could buy silica gel online, it's very cheap. Avoid temperature variations and the gel is not necessary.
4. Clean up procedure
This is the procedure recommended by Optic Wave Labs:
I make mirrors but I don't coat them myself (yet) - however, I've found that procedure to work very well on both coated and non-coated glass.
A few minutes of initial soaking in water makes everything easier later on.
After soaking it, add a few drops of detergent and rub very gently with your clean fingertips or with a soft, clean, lint-free cloth. Don't put pressure on the mirror, just try to detach the dirt from mirror in the horizontal direction and let it wash off. Don't drag dust particles across the glass, just detach them and let them go; this is why fingers are better than cloth - because you can feel large particles coming off.
When done, wash off the detergent with lots and lots and lots of water.
Using tap water for most of the cleaning procedure is absolutely fine. If you can drink the water, it's fine for the mirror too. Don't use hot water if the mirror is cold, there's a very small chance of cracking it, especially with cheap, mass produced glass.
When you're done cleaning, rinse the mirror with distilled water. Again, a few water spots on the mirror don't matter to performance, but the mirror looks better if it's spot-free. Tap water tends to leave water spots if you don't follow up with distilled water rinsing, and most people find the spots not pleasing from an esthetic perspective (but performance is same). So just splash a bottle of distilled water on it at the end and you'll be fine. No touching after rinsing.
Some dirt or mold may not be removed by the usual water-based procedure. In that case, use isopropyl alcohol, the highest concentration you can find (over 90% is fine). Rub gently with your clean, non-greasy fingertips or a lint-free cloth. If it doesn't come off quickly, leave it alone. Alcohol has probably killed the mold anyway.
Acetone might be used for things that resist even alcohol. But again, you have to use your judgement: a few little spots won't affect performance, so is it worth the trouble?
In any case, rinse with distilled water at the end, then let it dry off in an inclined position (carefully to not tip the mirror over on its face). Put a towel on the table in front of the mirror, so if it does topple over, at least it falls on something soft. Do not let it dry in a horizontal position, you'll get water spots and dust.
If there's some permanent damage in a few little spots, don't worry about it. The mirror will work essentially the same.
It is recommended that you do the water-based procedure every 1 or 2 years, depending on how dirty the mirror is. If dust contamination is moderate, leave it alone.
After everything is done, re-collimate the telescope carefully. But this should go without saying, since collimation is part of the regular maintenance of newtonian telescopes.