You can build a finite state machine with only 2 states to solve your problem:
def pesquisar( seq, inicio, fim ):
    estado = 0
    ret = []
    aux = []
    for x in seq:
        if estado == 0:
            if x == inicio:
                aux = [ x ]
                estado = 1
        elif estado == 1:
            aux.append( x );
            if x == fim:
                ret.append(aux)
                estado = 0
    return ret
sequencia = ['CGC','UUC','GCU','UUG','GAA','AAU','UUG','UGU','GUU','UUU','UGU','GGC','UGC','UCG','CUG','CUC','AAA','UUG','UUC','GCU','GCU','UUU','UGU','GUC','CUG','GCU','GCU','UUU','AUU','AUU','UUA','CGC','UGC','UUG','GCG','CUG','CUY','UUA','CGC','UGC','UUG','GGC','UUG','UUG','UGG','CUU','UGG','UUG','UUU','GUU','UAU','UAY','GCU','GCU','CUU','GUU','GUU','GUU','GCU','UGU','UGU','GCC','UAU','GGC']
print(pesquisar( sequencia, inicio = 'UGU', fim = 'UGC' ))
Exit:
[['UGU', 'GUU', 'UUU', 'UGU', 'GGC', 'UGC'],
 ['UGU', 'GUC', 'CUG', 'GCU', 'GCU', 'UUU', 'AUU', 'AUU', 'UUA', 'CGC', 'UGC']]
EDIT:
State machines can be built in Python with the use of yield, follows an alternative way of solving the problem with an even more compact code:
def pesquisar( seq, inicio, fim ):
    ret = []
    for i in seq:
        if i == inicio or ret:
             ret.append(i)
        if i == fim and ret:
            yield ret
            ret = []
sequencia = ['CGC','UUC','GCU','UUG','GAA','AAU','UUG','UGU','GUU','UUU','UGU','GGC','UGC','UCG','CUG','CUC','AAA','UUG','UUC','GCU','GCU','UUU','UGU','GUC','CUG','GCU','GCU','UUU','AUU','AUU','UUA','CGC','UGC','UUG','GCG','CUG','CUY','UUA','CGC','UGC','UUG','GGC','UUG','UUG','UGG','CUU','UGG','UUG','UUU','GUU','UAU','UAY','GCU','GCU','CUU','GUU','GUU','GUU','GCU','UGU','UGU','GCC','UAU','GGC']
print(list(pesquisar( sequencia, inicio = 'UGU', fim = 'UGC')))
Exit:
[['UGU', 'GUU', 'UUU', 'UGU', 'GGC', 'UGC'],
 ['UGU', 'GUC', 'CUG', 'GCU', 'GCU', 'UUU', 'AUU', 'AUU', 'UUA', 'CGC', 'UGC']]
							
							
						 
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– Woss
In this example string contains no occurrence of `UAG'.
– Bruno Camargo
Your example data does not have the sequence
UAG UGG GAU UUA UAA, right ?– Lacobus
What if you find multiple sequences? Or stop when you finish the first one?
– Miguel
No, my example does not have the sequence.
– 2583estbarreiro