"Like as a mighty grampus, when assailed and buffeted by roaring waves and brawling surges, still keeps on an undeviating course, rising above the boisterous billows, spouting and blowing as he emerges, so did the inflexible Peter pursue, unwavering, his determined career, and rise, contemptuous, above the clamors of the rabble."
-- Knickerbocker's History of New York by Washington Irving, 1809.
The term 'grampus' is rarely heard these days, and it was not a formal term even when it was in common usage. It could refer to many types of small whale, usually either an Orca or large dolphin1. These days it most often refers to Risso's dolphin, whose formal Latin name is Grampus griseus; Risso's dolphin is the only species of the genus Grampus.
In the 1500s on through the 1800s grampus was a general term, referring to a 'grand fish' (probably from the Latin grandis piscis), and generally to those members of the Delphinidae family that did not have a beak-like snout. As such, they were the fish that came to the surface to snort and splash and spout. It might also have included the Beaked Whales, which generally do have snouts but are also larger and have distinctive protruding tusks, disqualifying them as dolphins in the eyes of sailors. The grampus was not quite a sea monster, but it existed in the same general category.
The splashing and spouting were very much a part of the grampus image, so much so that sailors might call a person given to puffing and blowing a grampus2, and the the phrase 'to blow the grampus' meant to pour water over a sleeping or drunken sailor in order to rouse him.
Footnotes:
1. specifically, any large member of the Delphinidae family; the sailors recognized 'regular' dolphins as a familiar species.
2. Hence the usage in The Pickwick Papers by Charles Dickens, when Mr. Weller calls the houseboy as grampus because of his noisy huffings and puffings when eating.