Gaskell, a lawyer's son, was born at Naples in Italy and graduated in mathematics from Cambridge University in 1869. He then studied medicine at University College Hospital, London, but returned to Cambridge to serve as lecturer in physiology from 1883 until his death. His first studies investigated whether the heartbeat is under external nervous control or is an inherent property of the cardiac musculature (myogenic). Skillful work with tortoises and crocodiles showed that the heart's rhythm is indeed myogenic.

Gaskell also greatly increased knowledge of the structure of the autonomic (involuntary) nervous system. In 1886 he noted three major ‘outflows’ of nerves from the spinal cord and lower part of the brain: the cervico-cranial, thoracic, and sacral. On leaving the central nervous system each nerve passes through a ganglion, or relay station, sited alongside the spine. Gaskell discovered two key properties of the system. He first noted that the nerves of all three groups are enclosed in a white sheath of myelin before entering their adjacent ganglion; on leaving the ganglion however the nerves of the thoracic outflow have lost their sheath in contrast to the still myelinated nerves of the other two outflows. He had thus succeeded in finding a simple anatomical distinction between the myelinated nerves, sacral and cervico-cranial, of the parasympathetic system, and the unmyelinated nerves, thoracic, of the sympathetic nervous system.

He also noted that most parts of the body receive nerves of both types and that their actions seem to be antagonistic. That is, while the myelinated nerves of the parasympathetic system inhibited the action of involuntary muscle, those of the sympathetic system seemed to increase its activity. Although much of Gaskell's work was done on reptiles he realized it had wider implications and boldly predicted that it would apply also to mammals, a prediction soon confirmed. His work was published posthumously in The Involuntary Nervous System (1916).

Much of Gaskell's later life was spent studying mammalian evolution. He tried to show how mammals could have evolved from arthropods rather than echinoderms (the orthodox view). His ideas were published in The Origin of the Vertebrates (1908), which contains the results of 20 years' work, but his theories have been largely ignored.