Aspartame is broken apart in the intestinal lumen, which is the cavity where food passes through as it's digested. Digestive enzymes called esterases break the aspartame down into methanol, and peptidases release aspartic acid and phenylalanine. The two amino acids and methanol enter the cells lining the intestinal walls and are absorbed into the blood stream.
Sometimes only the methanol is split off the aspartame. The aspartic acid and phenylalanine remain bonded together as a single molecule called aspartylphenylalanine dipeptide. The methanol and bonded amino acid pair enter the mucosal cells where the amino acids are broken apart by the same enzymes found in the lumen.
Whole aspartame molecules can also be absorbed into the intestinal wall cells. In this case, the methanol and amino acids are split apart in the cell, then absorbed into the blood. No matter where the aspartame molecules are digested, only the amino acids and methanol enter the blood; aspartame is not absorbed into the blood intact.
The presence of methanol is a concern for some people -- however, consuming one aspartame-sweetened beverage generates 55 mg methanol/L, while the metabolism of fruit juice in your body produces 680 mg/L. Formaldehyde is also naturally found in many other foods and produced normally in the body. So, basically, aspartame digestion and metabolism provide a trivial amount of formaldehyde and formic acid.
Studies conducted on humans and animals using various dosages of aspartame indicate that absorption of the phenylalanine and aspartic acid have little effect on total plasma amino acid levels, or on brain amino acid uptake. Aspartame has no effect on blood fat or glucose levels, and doesn't change the amount of any gastrointestinal secretions made by your digestive system.
Magnuson BA, Burdock GA, Doull J, Kroes RM, Marsh GM, Pariza MW, Spencer PS, Waddell WJ, Walker R, Williams GM. "Aspartame: a safety evaluation based on current use levels, regulations, and toxicological and epidemiological studies." Crit Rev Toxicol. 2007;37(8):629-727.