The following document on the two kinds of mortification is taken from the compiled work called, Articles and Manuscripts of Dominic Farrell.
External Mortification
The point of mortification is quite simply to grow in grace, in the spiritual life, to live more to God and less to ourselves.
There are many things, both within and outside ourselves which serve to weigh down and prevent our spiritual progress. For example, I may see the benefits of temperance, but I am intemperate, I may see the benefits of prayer and spiritual reading but I am slothful, I may see the advantages of being calm and recollected but I am impulsive, passionate and a lover of distraction. I may want to be kind, cheerful and charitable, but I have a habit of being cold, gloomy and snapping at people when I feel annoyed. And so it goes on.
Basically, I am an unmortified person, or at least, I have not mortified, detached or as it were ‘died’ to temporal things and to myself sufficiently in order to reach holiness.
Many things in my life are preventing me from doing what God wants of me, preventing me from sanctifying myself. So external mortification consists in cutting off and restraining myself in regard to the outward things that slow down my spiritual progress. For example, not allowing the body to have all it wants all the time.
Going without some lawful pleasures, working physically for a long time when the body would rather rest or slouch around. Enduring cold or heat without immediately complaining. Saying ‘no’ to self every now and then instead of always pampering the senses. External mortification can also be called The Mortification of the Senses.
If the senses are not mortified we can never enjoy the calmness and peace of the Holy Ghost in the soul. For this is something interior and the constant and immoderate indulgence of the senses, draws us to what is exterior and so we never enter into ourselves where God shares His life with us.
Now it is recommended, especially for those who are still very new to the spiritual life, that they should be prudent and only exercise moderate exterior mortification. Going too far or taking on too much is both dangerous and unnecessary.
Internal Mortification
Interior mortification is something more hidden and more spiritual. It is easier to mortify ourselves interiorly if we are also mortified exteriorly and have our senses under the control of reason (that is, reason illumined or orientated by faith). It can be harder to restrain yourself from some interior impulse such as a flare of anger, envy, jealousy or an unkind thought, than to go without a tasty cake for example.
Generally, an interior act of mortification touches you more deeply and is harder to achieve. But for this very reason it is more sanctifying, because remember, the more a man overcomes himself, the closer he gets to God—there is less tendency to do his own will, to follow exclusively his own way in everything at the cost of ignoring and resenting God’s will. Remember, there cannot be union, harmony and interactive love between a man and God if the man stands in opposition to God by an unmortified disposition or self-willed attitude.
A man needs to work by degrees, to try to better himself each day and be more generous with God and less shut off from Him. The more generous he is with God, the less he will go against God (or we could say, refuse his obedience to God) and the more he will mortify himself in order to please and obey God. (Obeying God basically means keeping His commandments and doing our religious duties faithfully).
So the interiorly mortified person is able to stifle countless little inner motions towards anything that is either sinful or is likely to end in sin, or at least be of no profit to the soul. He mortifies inordinate self-love. Many people are quite clueless and careless as to where their affections lie and what it is that motivates them to do whatever they do. Fore example, a man won’t go to the trouble of robbing a bank if his heart is not in it—if money is not at the centre of his affections. But if he is very much an avaricious person, then he will be more inclined to go overboard and steal.
Again a devout person may not be very upset when some temporal good is taken away from them, whereas a more earthly minded person may become very cross, restless and passionate about it. St Gerard Majella was said to be the most mortified monk in his monastery, but he was also the most happy and joyful, because mortification leads to God.