• Overall survival (OS) rate [ Time Frame: At 2 years following enrollment ]
  -Patients that have died from any cause will be censored from the OS rate calculation
• Pathologic complete response rate (pCR) [ Time Frame: At the time of surgery (approximately 19 weeks) ]
  -Defined as the lack of viable cells observed in resected tumor tissue following neoadjuvant therapy and will be determined by an experienced sarcoma pathologist
• Rate of acute treatment-related grade 3 or higher toxicity defined by CTCAE version 5.0 [ Time Frame: Through 90 days of completing treatment ]
• Rate of late treatment-related grade 3 or higher toxicity defined by CTCAE version 5.0 [ Time Frame: At 2 years following enrollment ]

• Drug: Paclitaxel
  -Commercial supply
  Other Name: Taxol
• Radiation: Radiation therapy
  -Patients may be treated with electrons, 3D conformal photon radiotherapy, intensity modulated photon radiotherapy (IMRT), proton radiation therapy, or a combination of these.
• Procedure: Research blood draw
  -Within 1 week (prior to cycle 1 of paclitaxel preferred but not required), pre-radiation therapy (any time weeks 5-7 as long as radiation therapy has not started), post-radiation therapy (day of last fraction), 14 days post-radiation therapy, and within 2 weeks post-surgery

Inclusion Criteria:

• Histologically or cytologically confirmed cutaneous angiosarcoma.
• Measurable disease defined as lesions that can be accurately measured in at least one dimension (longest diameter to be recorded) as ≥ 5 mm with CT scan or ≥ 5 mm by clinical exam at the time of diagnosis
• Currently receiving or planning to receive weekly paclitaxel for 12 weeks at 80 mg/m^2 weekly. The patient must be able to begin radiotherapy within the first 7 weeks of paclitaxel treatment.
• At least 18 years of age.
• ECOG performance status ≤ 1
• Women of childbearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control, abstinence) prior to study entry and for the duration of study participation. Should a woman become pregnant or suspect she is pregnant while participating in this study, she must inform her treating physician immediately. Men treated or enrolled on this protocol must also agree to use adequate contraception prior to the study, for the duration of the study, and one month after completion of the study
• Ability to understand and willingness to sign an IRB approved written informed consent document (or that of legally authorized representative, if applicable).

Exclusion Criteria:

• Patients deemed ineligible for curative therapy by the treating medical oncologist, radiation oncologist, or surgeon.
• A history of other malignancy ≤ 3 years previous with the exception of basal cell or squamous cell carcinoma of the skin which were treated with local resection only or carcinoma in situ of the cervix.
• Currently receiving any investigational agents.
• Current central nervous system disease or distant metastatic disease not including local-regional lymph nodes or satellite lesions. Patients with known brain metastases must be excluded from this clinical trial because of their poor prognosis and because they often develop progressive neurologic dysfunction that would confound the evaluation of neurologic and other adverse events.
• Grade 2 or greater neuropathy
• A history of allergic reactions attributed to compounds of similar chemical or biologic composition to paclitaxel or other agents used in the study.
• Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, or cardiac arrhythmia.
• Pregnant and/or breastfeeding. Women of childbearing potential must have a negative pregnancy test within 14 days of study entry.
• HIV-positive patients whose CD4+ T-cell count is < 350 cells/mcL.