Homebrew: Warrior of the Arcane Blood. It combines the monk's fighting style with magic. I'd love to hear your thoughts

• Martial Proficiency. You gain proficiency in one skill of your choice from among Arcana, History, or Insight.
• Cantrips. You learn three cantrips of your choice from the Sorcerer spell list. You learn an additional sorcerer cantrip at 10th level, as shown in the table.
• Spell Slots. The table shows how many spell slots you have to cast your spells of 1st level or higher. To cast one of these spells, you must expend a slot of the spell’s level or higher. You regain all expended spell slots when you finish a Long Rest.
• Spells Known of 1st Level and Higher. At 3rd level, you know three 1st-level spells of your choice from the Sorcerer spell list. Whenever you gain a level in this class, you can replace one of the sorcerer spells you know with another spell of your choice from the sorcerer list, which must be of a level for which you have spell slots.
• Spellcasting Ability. Wisdom is your spellcasting ability for your subclass sorcerer spells, as you tame your chaotic magic through willpower and mental discipline. You use Wisdom whenever a spell refers to your spellcasting ability.

• Spell Save DC = 8 + your Proficiency Bonus + your Wisdom modifier
• Spell Attack Modifier = your Proficiency Bonus + your Wisdom modifier

• Action Conversion. When you cast a spell from this subclass that normally requires a Bonus Action, you can choose to cast it as a Standard Action instead.
• Arcane Attack. When you take the Attack action on your turn, you can replace one of your physical attacks with the casting of a cantrip from this subclass that has a casting time of 1 Action. When you take the Attack action on your turn, you can replace one of your attacks with a spell of 1st-level or higher from this subclass.

• Innate Stunning Smite. When a creature takes damage from one of your subclass spells or cantrips, or fails a saving throw against it, you can spend 1 Focus Point to activate your Stunning Strike on that target through the magic of the spell.
• Arcane Metabolism. When you use your Uncanny Metabolism core class feature, the rush of energy revitalizes your magic. In addition to regaining your Focus Points, you regain expended spell slots whose combined level is equal to or less than your Proficiency Bonus (for example, at 11th level with a +4 Proficiency Bonus, you can regain four 1st-level slots, or two 2nd-level slots).

• Arcane Flurry of Blows. When you use your Flurry of Blows, you can replace one of those three unarmed strikes with the casting of a cantrip from this subclass, regardless of whether the cantrip normally requires an Action or a Bonus Action. When you use Flurry of Blows, you can spend 1 additional Focus Point to replace one of your Unarmed Strikes with casting a cantrip, regardless of its casting time.
• Arcane Patient Defense. When you expend a Focus Point to use Patient Defense, the protective aura of your blood expands to shield your allies. In addition to gaining temporary hit points for yourself, you choose up to three willing creatures within 30 feet of you: each immediately gains temporary hit points equal to a roll of your Martial Arts die + your Wisdom modifier.
• Arcane Step of the Wind. When you use Step of the Wind and spend Focus to teleport, you can choose one willing creature within 5 feet of you and teleport it along with you to an unoccupied space at your destination. The transported creature gains Advantage on its next attack roll made before the end of its next turn. If you instead choose to teleport alone without bringing anyone along, the repressed magic explodes at your destination: each hostile creature within 10 feet of the space you appear in must succeed on a saving throw against your Monk DC or take Force damage equal to two rolls of your Martial Arts die.
• Arcane Step of the Wind. When you expend a Focus Point to use Step of the Wind, you can choose one willing creature within 5 feet of you and teleport it along with you to an unoccupied space at your destination. The distance of this teleportation is equal to the movement granted by your Step of the Wind feature. If you instead go alone without bringing anyone along, the repressed magic explodes at your destination: each hostile creature within 10 feet of the space you appear in must succeed on a saving throw against your Monk DC or take Force damage equal to two rolls of your Martial Arts die.

What's up with the 17th level feature? Step of the Wind doesn't let you teleport, and this feature also doesn't let you teleport. If the intent is that this feature lets you teleport, you REALLY need to revise the wording.

Oh, my mistake—the translation didn't turn out right.

Arcane Step of the Wind. When you expend a Focus Point to use Step of the Wind,  you can choose one willing creature within 5 feet of you and teleport it along with you to an unoccupied space at your destination. The distance of this teleportation is equal to the movement granted by your Step of the Wind feature. If you instead go alone without bringing anyone along, the repressed magic explodes at your destination: each hostile creature within 10 feet of the space you appear in must succeed on a saving throw against your Monk DC or take Force damage equal to two rolls of your Martial Arts die.

The subclass's main issue is likely that cantrip damage scales with caster level, and replacing one or two attacks with them would be overpowered. 

• Arcane Attack (6th level). When you take the Attack action on your turn, you can replace one of your attacks with a spell of 1st-level or higher from this subclass.
• Arcane Flurry of Blows (17th level). When you use Flurry of Blows, you can spend 1 additional Focus Point to replace one of your Unarmed Strikes with casting a cantrip, regardless of its casting time.

What do you think of these changes?

I've no problem with that. The 1970's Kung Fu flicks had many Masters who were able to cast spells as well as do multiple kicks to the face.