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I would not cut off the growth, as the plant needs this to produce additional flowers next season. If you are experiencing an abundance of green growth, it could be too much nitrogen (a soil test will tell for certain). You can normally offset this in spring with a high phosphorus fertilizer, or bone meal, which will help encourage more blooms and bulb growth.

Muscari are planted in the fall. They form their roots in the fall, then bloom in the spring.

Here is an article with more information.

https://www.gardeningknowhow.com/ornamental/bulbs/grape-hyacinth/planting-and-care-of-grape-hyacinths.htm

I would not lose hope yet. Spring is just starting to get into gear, so I think with a little extra time you will start seeing the tender shoots of the grape hyacinth pop through the ground.

For more information on the care of grape hyacinths, please visit the link below:
https://www.gardeningknowhow.com/ornamental/bulbs/grape-hyacinth/planting-and-care-of-grape-hyacinths.htm

It looks like the confusion is widespread based on my research.

According to the ASPCA, the grape hyacinth is not poisonous to cats or dogs.

http://www.aspca.org/pet-care/animal-poison-control/toxic-and-non-toxic-plants/grape-hyacinth

As for toxicity to humans, the University of Wisconsin, California and Utah published poison prevention literature that said it was not toxic.

Store the bulbs in a cool, dry place for the summer, then plant them in your flower garden early in the fall.

For more information on the care of grape hyacinth, please visit the following link:
https://www.gardeningknowhow.com/ornamental/bulbs/grape-hyacinth/planting-and-care-of-grape-hyacinths.htm

Yes, and these article will help with storing, depending on your location: https://www.gardeningknowhow.com/ornamental/bulbs/bgen/preparing-bulbs-for-winter-how-to-store-bulbs-for-winter.htm
https://www.gardeningknowhow.com/ornamental/bulbs/bgen/storing-bulbs-in-south.htm