As stated above, must the duration of an imbibed Mutagen be continuous or can it be divided like many other class abilities (into 10 minute increments at low levels and in 1 hour increments at L14 with Persistent Mutagen)?
The Mutagen ability does not mention anything like that, so it works continuously.
Upon being imbibed, the mutagen causes the alchemist to grow bulkier and more bestial, granting him a +2 natural armor bonus and a +4 alchemical bonus to the selected ability score for 10 minutes per alchemist level.
Persistent Mutagen (Su) At 14th level, the effects of a mutagen last for 1 hour per level.
However, keep in mind that the mutagen does not have anything saying it can only be created once per day. Meaning that, as long as you spend another hour brewing another mutagen, you could make multiple mutagens in a single day.
You simply cannot have two doses of mutagens available at once, unless you learn the Infused Metagen discovery, which allows you to keep a second mutagen for emergencies.