To understand how this works, try passing the list '(3 7 6 1 5 2 4) into mergesort and trace the mergesort function. You can do this by using:

(require (lib "trace.ss"))

in DrScheme and then, after copying and pasting in the mergesort code, do:

(trace mergesort)

Below is a fully functional mergesort in Scheme:

(define (mergesort l)
   (cond ((< (length l) 2) l)
         (else (merge (mergesort (partition1 l))
                      (mergesort (partition2 l))))))
   
(define (merge l1 l2)
   (cond ((null? l1) l2)
         ((null? l2) l1)
         ((< (car l1) (car l2))
            (cons (car l1) (merge (cdr l1) l2)))
         (else (cons (car l2) (merge l1 (cdr l2))))))
          
(define (partition1 l)
   (let ((num-elements (round (/ (length l) 2))))
      (define (part counter l)
         (cond ((= counter num-elements) ())
               (else (cons (car l) (part (+ counter 1) (cdr l))))))
      (part 0 l)))

(define (partition2 l)
   (let ((num-elements (round (/ (length l) 2))))
      (define (part counter l)
         (cond ((= counter num-elements) l)
               (else (part (+ counter 1) (cdr l)))))
      (part 0 l)))