The features of the bound feature are suppressed by an antimagic field.
The effects bound to the amulet do not operate while in an antimagic field. The field itself limits but doesn't complete abate the spell casting feature. The construct can still understand verbal commands as per its language stat block.
Antimagic affecting a monster's features
The effects of antimagic field relevant here are:
Spells. Any active spell or other magical effect on a creature or an object in the sphere is suppressed while the creature or object is in it.
Targeted Effects. Spells and other magical effects ... that target a creature or an object in the sphere have no effect on that target.
Sage Advice Compendium addresses monster features on page 18 while discussing a dragon's breath weapon feature. In short determining if a feature is suppressed by antimagic field:
- Is it a magic item?
- Is it a spell? Or does it let you create the effects of a spell that’s mentioned in its description?
- Is it a spell attack?
- Does its description say it’s magical?
"If your answer to any of those questions is yes, the feature is magical" in the sense that it will be suppressed by antimagic field. There is Q&A here that goes into more depth about magical features and anitmagic field interaction.
Bound feature (amulet) is suppressed
The amulet effect of the shield guardian is explicitly magical.
The shield guardian is magically bound to an amulet.
The magic of the amulet is suppressed while either the amulet or the guardian is in the field due to the bidirectional nature of the effects. While the guardian is in, it can't be the target of the magical effects. While the amulet is in the field, it can't use it's magical properties nor be the target of the magical effects.
The benefits of this bond which are suppressed:
- telepathically call the guardian to travel to it
- the guardian knows the distance and direction to the amulet
- If the guardian is within 60 feet of the amulet's wearer, half of any damage the wearer takes (rounded up) is transferred to the guardian.
Storing & Casting Spells with the Guardian
- The field prevents the guardian from casting stored spells while it's
in the field.
- It prevents the caster from putting a new spell in if either of them are in the field.
Stored spell can still be cast if guardian is outside the field
The guardian can be a kind of contigency caster that is not dependent on the caster nor amulet, so that still functions and the guardian can still cast those spells.
... when a situation arises that was predefined by the spellcaster, the guardian casts the stored spell ...