I'm answering this question from general perspective and not being specific to Lord Parashurama. It is because other incarnations of Lord Vishnu also show anger many times.
For eg. Lord Rama becomes very angry with ocean when ocean doesn't come to adress prayer of Rama. (Valmiki Ramayana VI.21)
Lord Nrisimha is also very angry with Hiranyakashipu:
Manifesting a full effulgence and a fearsome countenance, Lord Nrsimha, being very angry and finding no contestant to face His power and opulence, then sat down in the assembly hall on the excellent throne of the king. Because of fear and obedience, no one could come forward to serve the Lord directly. (Srimad Bhagvatam 7.8.34)
Similarly we find Lord Krishna is also angry in certain parts of Mahabharata. And not only to incarnations of Lord Vishnu, we find incarnations of Lord Shiva also show anger. For eg. Sage Durvasa. Similarly the Sata-Rudriya prayer itself starts from - 'Namaste Rudra Manyava' / 'Salutations to thy anger Oh Rudra'
So, a question arises 'Can Lord Become Angry?
Regarding this Srimad Bhagvatam states:
For persons with impure vision, the Supreme Lord's eyes appear like those of someone who indiscriminately drinks intoxicating beverages. Thus bewildered, such unintelligent persons become angry at the Supreme Lord, and due to their angry mood the Lord Himself appears angry and very fearful. However, this is an illusion. When the wives of the serpent demon were agitated by the touch of the Lord's lotus feet, due to shyness they could proceed no further in their worship of Him. Yet the Lord
remained unagitated by their touch, for He is equipoised in all circumstances. Therefore who will not worship the Supreme Personality of Godhead? (Srimad Bhagvatam 5.17.20)
But, again there is a question whether attributes like anger are only shown by Gods (ie. Devatas) or by forms of Supreme Lord also?
The answer is it can be shown by Supreme Lord also. For eg. Katha Upanishad says Gods fear of Lord's nature:
2-III-3. For fear of Him, fire burns;
For fear of Him, shines the sun;
For fear of Him, Indra and Vayu function;
For fear of Him, death, the fifth, stalks on the earth.
One may ask Is there an Explicit Shruti proof that Brahman described in Upanishad is stated to be angry?
The answer is yes. For eg. Svetasvatara Upanishad IV.22 states:
मा नस्तोके तनये मा न आयुषि
मा नो गोषु मा न अश्वेषु रीरिषः ।
वीरान् मा नो रुद्र भामितो
वधीर्हविष्मन्तः सदामित् त्वा हवामहे ॥
Injure us not in respect of children, grand-children and life, nor in respect of cows and horses. Do not destroy our heroes in Thy anger, O Rudra. We invoke Thee always with offerings.
So, it is already proved Supreme Lord can show anger also.
Is there any benefit of anger of Supreme Lord?
Yes, anger of Supreme Lord can also act as grace of Lord. I remember Shiva Purana statement that 'Anger of Rudra is better than Grace of other Gods.' I'm not exactly able to locate where it is this time. (I'll update if I find.) Similarly, as I discuss in this anger sage Agastya tells about benefit of Ramas anger too:
O king, all the monarchs, slained by Janarddana,holding discus and the lord of the triple world, ained to his own region; even his anger becometh like a boon.
Thus Supreme Lord (being Purusha) can associate himself with various Prakirti elements (like satwa-rajas-tamas) and can show anger like attributes also.