Reading Beastform Mutagen, it says that you choose from the abilities listed in the referenced spell. In all four cases (Alter Self, Beast Shape I-III) the spell has a listing of the abilities it can grant; the size change isn't part of that, but precedes that list. So by RAW, I'd say no - you can't choose\don't get the size change; you just grow claws, gain darkvision, grow wings, etc.
From a house rule perspective I would probably allow you to choose the size change as an ability, but it would use up one of the ability choices granted by the mutagen.
The only RAW way I can think of for a mutagen itself to change a beastmorph alchemist's size is through the master chymist advanced mutagen Growth Mutagen. However, enlarge person is on the alchemist's extract list, along with reduce person.
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So for clarification purposes, when an Alchemist with the Beastmorph Archetype uses their 3rd level mutagen, they can or cannot assume a Small or Medium size?
"The beastmorph also gains his choice of one of the abilities listed in the alter self spell, which persists as long as the mutagen." Each of the listed spells refer to a list. Size, ability score bonuses, and natural armor bonus is never part of that list.
The list of selectable abilities at 3rd level is "darkvision 60 feet, low-light vision, scent, and swim 30 feet."
At 6th level, the list is "climb 30 feet, fly 30 feet (average maneuverability), swim 30 feet, darkvision 60 feet, low-light vision, and scent."
At 10th level, the list is "climb 60 feet, fly 60 feet (good maneuverability), swim 60 feet, darkvision 60 feet, low-light vision, scent, grab, pounce, and trip."
At 14th level, the list is "burrow 30 feet, climb 90 feet, fly 90 feet (good maneuverability), swim 90 feet, blindsense 30 feet, darkvision 60 feet, low-light vision, scent, constrict, ferocity, grab, jet, poison, pounce, rake, trample, trip, and web."
Not a single thing that I didn't just write in blue is selectable, period. The mutagen does what it usually does, plus the one to four abilities you selected. That's it.