Your mom's cousin is your first cousin, once removed.
Here's a breakdown of what that means:
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First Cousin: First cousins share a common set of grandparents. You and your mom's cousin don't share grandparents, but your mom and her cousin do.
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Once Removed: "Removed" indicates a difference in generation. Because your mom and her cousin are in the same generation (i.e., your mom's cousin is not your parent or child), you are one generation removed from the first cousin relationship, hence "once removed." Your grandparents are also the great-grandparents of your mom's cousin. You share direct blood relatives (your grandparents are also their great-grandparents) even though there is a generation difference.
Think of it this way: your parent's first cousin is also the first cousin of your aunts and uncles. If you have an aunt or uncle who had a child, their child would be your first cousin. Your mom's first cousin is in the same generation as your aunts and uncles, not in your generation, so they're "once removed" from you.
